205,000 troops (and robots) should be well enough to capture a city of seven million people. Imagine a quarter of the population is military aged males or whatever so it's ten to one at best numbers wise if they're pressing everyone into service. And there's no way that's happening I feel.
Most of the largest gangs have memberships ranging between low hundreds to low thousands and there's like a dozen of them. I'd be surprised if you total the gangs, police and corporate security if it adds up to a hundred thousand or so combatants.
Hm. Quick google assuming were talking 2077 as the most familiar version of night city,
its wiki page suggests pop of about 6 million people. The basic rule of thumb for an insurgency generally seems to be something around a 50-1 ratio. So, 6 million people would like to have at least 120k occupation army.
However, that's for occupation, not conquest. Conquest then we have to worry a bit less about the population, and more about space. Also according to the wiki, the city occupies about 75 km^2.
This suggests its about 10 km wide, which lines up with measuring the real life location its based on. On the one hand this isn't a lot of frontage to man overall, even at 1,000 men per km that would only be about 10,000 people to hold the front fairly strongly. That however is to the attackers great disadvantage, because it also means 10,000 defenders can also hold the cities permitter quite strongly too.
This is a problem for the Fallout army, since it actually might mean the front is too narrow to effectively make use of their numbers. Assuming the actual city government had even 1% of its population it could reasonably call up, that's some 60,000 people available to man the parameter, which sea to sea with rounding up to a 100 km^2 that needs protected is still only a perimeter of maybe 40 km. Which would allow a troop density of about 1,500 per km, or higher than 1 per meter. Obviously you'd do something less dense with any level of organization, say one guy per 10 meters, but that means the front line can be potentially held with merely 4,000 people deployed to that front. Then obviously the rest held back to steadily feed into the front lines as casualties mount there, or on fall back lines. And this much area being protected suggests the defense of the city is starting something like 3-5 km out from the city itself in the badlands, so there is actually space to fall back into steadily tougher defensive grounds.
So, a mere 50,000 could quite potentially man 10 defensive lines to a fairly strong degree. And because the front is so narrow, the Fallout people don't have much other choice than bashing into those lines head on, either trying for frontal assaults into entrenched infantry, which is something even not particularly well drilled troops are capable off, or trying to grind Night city out in a siege, which at least in the initial list they don't seem to have the particularly heavy artillery you'd like for that. If the artillery is only about 10 km range, it might be possible to hold the Americans back enough for some time to keep the docks and certainly the spaceport out of easy artillery range.
And if you have a long siege, especially if the docks stay somewhat functional, then Night cities numbers, wealth, and connections can start coming in. Given time you can eventually mobilize, say 10% into various guard formations of various levels of loyalty getting some 600,000 under arms, outnumbering the invaders some 3-1, and with the docks keep importing more heavy weaponry/mercenaries.
Probably bad for the local area to have half a million armed men in all their own little regiments, but that gang war/power struggle is future Night Cities problem.
So, even attacking shoulder to shoulder over the 10 km front the Americans can only throw about 10,000 men at once at the city. An attack with 10-20k on the front would literally be talking about attack densities like the NCR in the below Sodaz video, across the entire front.
So, likely no one attack, between automatic weapons fire and any artillery the Nighters have, can involve more than about 5-20k people. Any more density is just asking for unnecessary casualties. Which also means the defenders never have to be able to hold against more than about 20k at once, despite the potentially quite lopsided overall numbers.
This is then the potential battle of thermopile situation: 20k good soldiers can hold off 200k okay ones, because the numbers can't be properly brought to bear: a 10-1 numerical advantage instead manifests as several rounds of 1-1 combat, where individual skill can much more manifest. I could easily see Night City having 20,000 well equipped and at least somewhat disciplined people.
I don't think the virtibirds help too much: I think they can carry about 6 people, so 300 of them can at most deploy some 1,800 people, which likely isn't enough to overwhelm locals all that much. Plus the relatively small size of the area hurts them again. A modern stinger missile has something like a 5 km range against helicopter level threats. Which means 1 Stinger missile team in the core of the city could potentially cover the entire city! I think there is probably a lot more than 1 team equipped with Stinger level equipment. And Night city is not lacking in airborne assets.
I know less about Cyberpunk than Fallout, but the battlefield is so constrained that I think the force assembled would be pretty poor on the target. I'm not sure they will actually be able to penetrate into the city core before petering out.
Edit:
@Husky_Khan , where are you getting 200,000? Isn't it 5 divisions of about 20,000, so about 100,000 combat troops, plus whatever the number of support troops would be?