and if Cortana gets into the Deathstar's central computer core.......... That alone is the things of nightmare fuel.
I'm not sure Cortana is all that impressive in Star Wars? She's a high-level software AI... in a setting where AIs are a dime a dozen. For all we know, R2 has more processing power than she does (bearing in mind, R2 is, quite literally, a rolling supercomputer, as his primary function is an Astromech meant to make highly complex and accurate multidimensional physics calculations quickly... that is some serious processing power). C3P0 may also have comparable processing power and a database that is, well, frankly, enormous, as he is a natural language translation AI able not just to immediately and dynamically translate multiple forms of communication around him, but also to rapidly construct a new linguistic database and use it to communicate on the fly (as seen in RotJ with the Ewoks).
I think you might be well underestimating the actual processing power of Star Wars given when stated roles Droid perform. Cortana is unlikely to be able to do any better than R2, and in point of fact, may well be able to do nothing at all as the internal computer engineering may well be completely incompatible with her programming to the point where she might as well be trying to hack a physical book.
This lack of technological similarity may also hinder the other "smart" characters brought over. Sam is brilliant, but she lacks a lot of the base line technical knowledge to provide immediate improvements and would have to study up on the underlying physics and tech before she can begin to push things forward (which, I do think she CAN, but it's not going to be an immediate thing). Batman is in a similar situation, his gear and tech is balanced towards dealing with DCAU tech, which is supposed to be more or less earth based tech. That said, in a twist, I think Batman is actually the less useful persona here. He's just another combat / infiltration specialist and while he might be more capable than anyone in the rebellion, he has an entire different set of skills that it appears that is even in shorter supply with the Rebellion: business savy. Bruce Wayne I think is actually the more valuable. Give Bruce some seed money or implant him in a Rebel backing corporation and let him loose to organize and wheel and deal and the Rebellion actually gets considerably more resources and equipment than they already had.
Now, for the specific mission they are one: the Rescue of Princess Leiah. What do they bring to the table and how much can they change things...
SG-1 Team (Stargate SG1 circa Season 8) - Not a huge amount in the immediate moment, in fact, this many extra bodies make it a lot harder for the team to infiltrate the Death Star and rescue Leiah. Assuming they CAN hide all the extra bodies and succeed on infiltration, SG-1 is best used to hold down the Millenium Falcon and keep it ready for departure.
Master Chief and Cortana Circa Halo 2 - As part of the initial infiltration team? Not super useful, they stand out to much. As I said, I don't think Cortana is anything special as far as AI power goes in Star Wars, and given that Star Wars weapons are mostly forms of directed plasma, which we know can harm MC's armor, he's not necessarily an invulnerable killing machine. And his armor is distinctive, making him unsuited for infiltration. So he gets kept behind to hold down the fort too. They might perhaps move him up to guard C3P0 and R2 in the control room though, and have Cortana perhaps piggyback with R2's hacking efforts, which may allow them some extra options.
Captain America (MCU circa Age of Ultron) - Cap. is probably one of the few people added to the infiltration team going with Luke, Han, and Chewie. They may have to leave the shield behind, though perhaps they can figure out a way to disguise it and bring it with them. Cap will bring a bit better tactical leadership to that team, though he's no better a liar than Han is, however, assuming they manage to bring his shield this means that when they get attacked rather than retreating into the garbage disposal, they can punch straight through the Stormtroops and retreat to their ship.
Batman (JLU Animated) - He's going to back up Obi-Wan in shutting down the shield generator, as both are much stealthier than the others in this team. This means that as things go hot and Vader starts pursuing Kenobi, Kenobi will have backup in the fight. Now, Batman is good, but he's not "beat Dark Vader" levels of good. He is, however, basically as equipped with crazy ass tricks as any Mandalorian, which means that rather than having to sacrifice himself to buy Luke and the others time to escape, he'll be able to provide critical distractions and moments to allow Ben and himself to evade Vader and get back to the Falcon.
I don't think they can actually do more damage to the Death Star in that initial situation than they did in the original movie, they don't have the prep time nor the technical understanding in the group to actually analyze the Death Star plans (Sam is smart, but she lacks even the foundational knowledge of Star Wars to BEGIN to understand what she's looking at and she doesn't even know what she doesn't know yet). Something a lot of folks are forgetting is that the Empire was purposefully
holding back when it came to letting Leiah escape. The Stormtroopers were under orders to let them escape and not kill them, as the main goal of the Empire was to track the Falcon back to the main Rebel base on Yavin, not stop them from escaping. Vader eliminated the one person who was a potential threat to that plan, Obi-wan. There's no reason to think that their plan will change here; however, they will have to go harder to do it, and not hold back anywhere near so much as they did originally.
The escape is... well, more violent than it was originally, the SG team and MC go active almost as soon as the infiltration goes sideways (look, Cap ain't going to do any better than Han on the radio call that triggers the situation going wrong). They punch straight back to the ship quickly. Meanwhile Batman and Kenobi kite Vader as much as possible, though they can't truly lose him due to him tracking Kenobi via the Force. Even so, with all of Batman's tricks, Vader is kept much more off balance as he doesn't have the same intimate knowledge of his opponent that he did of just Kenobi, so those two manage to escape.
The battle against the TIEs is a joke. The ball turrets likely being manned by Cap and someone from the SG team.
On the way back the team likely realizes that they've been had. Cap, Batman, and likely the SG team all realize that it was to easy, and so rather than head straight for Yavin, they instead head to some other out of the way station and do a deep search for the transponder that is being used to track them. Once that's removed (likely just as the Death Star shows up in system) and they manage to escape, again going to yet another non-rebel planet to wait and see if they've lost their tail and once they have, they head to Yavin to drop off Leiah and everyone who wants to join the Rebellion.
This means that the Rebels are no longer attacked at Yavin and have more time to organize. Han and Chewie head off with their payment without having a crisis of consciousness that leads them to join the Rebellion. Meanwhile the Rebellion leadership begins to integrate those who've joined them. Kenobi joins their senior command as an advisor and focuses on training Luke. The the combat members of the SG team and Cap join the Rebel commando units in their actions, greatly improving those units who they're with, putting further hurt to the Empire while the Rebels build up their strength for a surprise attack on the Death Star. Sam and the other scientists of the SG team move into R&D, quickly getting up to speed on SW tech and doing what they can to make improvements. Wayne meanwhile is quietly inserted into a major Corellian Corporation and quietly begins to consolidate business power to divert funds and resources to the Rebels.
Eventually the Rebels launch a surprise attack on the Death Star using strike craft much like their initial desperation raid, except with a lot more fighters and in a situation where they hold advantage. Likely they purposefully leaked a false position for their main base to draw the Death Star out, and then ambushed it. Luke still likely gets the killing blow on the Death Star using the Force much more adeptly than his by the seat of his pants moment in ANH (none of those brought over are excellent pilots and even experienced Rebel pilots failed to make the shot in ANH). It's a bloody battle, but the Rebels succeed and DON'T have to leave Yavin, allowing them to build up even further.
Without having to evacuate Yavin the events of ESB are completely derailed (you also lack Han being around, who's gone and paid off Jabba and gone back to his lazy smuggler's life... though he may regularly take jobs from the Rebels at this point for discrete transport and such). That said, it's plausible that the Empire uses a similar plan to find Yavin that they used to find Hoth, and eventually succeed. Yavin, however, is far better defended than Hoth was and has had much more time to dig in and prepare for siege. Plus with resources coming in from the new Correllian based Wayne Enterprises, they are much better equipped and have a strong space based force. Not enough to truly beat the Empire in a full blown space engagement, but enough that the Empire will have to actively rally their forces to strike... which will give the Rebels a head's up that the attack is coming and roughly when.
Thus they likely move the most important aspects of the Rebellion off Yavin and basically turn the entire place into another trap for the Empire. When the Empire's fleet arrives (likely something along the lines of a dozen or more Star Destroyers plus the Executioner), they are hit hard and fast, bleeding the fleet severely likely taking out a few of the Star Destroyers while only a handful of Rebel ships are lost. Meanwhile when the Empire makes landfall rather than the base, they find a place booby trapped all to hell and back while also having been sanitized of critical information. Thus the entire thing becomes an expensive and blood boondoggle on the part of the Empire.
Meanwhile the Rebel commando teams are constantly hitting critical infastructure of the Empire and between MC and Cap some of those teams seem to feature literally unstoppable warriors that begins forcing the Empire to shell out considerable money on elite bounty hunters to try and counter... likely unsuccessfully. At some point though the Emperor finally has had enough of those elite commando units and deploys Force users against them... which are the main weakness of those people.
However by this time Luke is much, MUCH more trained. He's likely gotten good enough fast enough to be a hard counter to things like the Inquisitors and low level Force Users the Emperor kept around. He's not up the Mandalorian S2 level Luke yet, but he's probably RoTJ level Luke. Meanwhile any force based assassins sent after Rebel high command just get punked by Obi-Wan "Hello There" Kenobi.
So, in the long term The Rebellion becomes more successful, but it's victories in some ways less dramatic. You are unlikely to see as many single pivotal moments, but in the long term they will slowly and systematically bleed the Empire dry.
