If this is following a general Russian pattern, I'm assuming the Fallout Americans will attempt a similar airborne operation, since that is what they do, to support their opening invasion. The Russians were able to use heliborne forces to strike as Hostomel Airport and drop a few hundred troops there, but there were heavy losses and the Ukrainians were able to counter attack and retake the airfield. Comparing the Vertibirds to Russian Helicopters, I honestly think the Russians probably have better capabilities as we know they have both utility/transport and attack helicopters will countermeasures and more longer ranged weapons and the like so I think Vertibird losses would be heavier. The advantage the Fallout Americans would have is they have robots and power armor potentially in that first wave, but I feel that they would eventually get swamped in the counterattacks.
The other issue is that the Fallout Americans will have to hold any airborne landing sites longer, including the Airport, because the Russian invasion force was initially fully mechanized with lots of armor and air support. The Fallout Americans MIGHT be as vehicle heavy, but there's no indication they'll be any less vulnerable to thirty kilometer long traffic jams. In fact, such outcomes might be more likely.
Unlike the Russians, the Fallout Americans won't benefit from widespread sabotage and infiltration as well as having years to waste on intelligence gathering and scouting and benefiting from having lots of connections across the border, and common language and cultural/religious practices as well. They'll be going in more blind, which can lead to any sort of road bound assault like the Russians attempted to likely be less successful and thus their advances by motorized/mechanized forces along roads pretty slowly.
The reason the Fallout Americans will be more successful then the Russians in part is that they won't be bound to the roads and military vehicles using them. Power Armored infantry can carry heavy weapons and robots like Gutsies and Sentry Bots and Assaultrons backed by lighter vehicles and Vertibirds can go across rougher terrain on a broader front and advance on that broader front, away from the roads and overwhelm Ukrainian defenses. The Russians when attempting to capture Kyiv kept trying to find alternate road routes to little avail in attempting to outflank the Ukrainians. The Fallout Americans can attack along a wider front, between the roads, through the wilderness, through the urban sprawl, as well as the roads and force the Ukrainians to spread their defenses thin.
And since you need heavy weapons to counter Power Armor and Sentry Bots/Assaultrons reliably, they'll have to spread out their RPG's and Javelins and NLAWs as well as artillery fire. And it's far harder deploying heavy weapons.... because they are heavy... off road and deploying them in the numbers they could intercepting road bound convoys and thunder runs.
Artillery will probably be the biggest killer of Fallout Americans though, but that is a finite amount and the Ukrainians only have the Tochka Ballistic Missiles at the moment, which aren't very accurate for tactical purposes. NATO would have to get them more artillery and stuff more quickly then waiting until May or June or whatever and by then I feel the War would be largely decided.
I think the Fallout Americans can take Kyiv in about a month with the rest of the country falling away in the following weeks sooner or later. It won't be easy, but Fallout America would be victorious I feel.
