To give my position on the issue, I have no problem with the NCR capitol being nuked as given it is a major population center with density, nukes are floating around in post war America and the NCR has no shortage of enemies, it's not unthinkable.
My only issue is this may mean New Vegas is being retconned and screw that.
So, let's just assume that Shady Sands got destroyed after the events of New Vegas and the year being earlier is misunderstood or a typo what does that mean for New California and New Vegas?
Well, if the NCR won that means New Vegas likely fell into chaos, although the families might be able to pick up the pieces but fighting over the top dog position will go on for years with no one to keep them in line.
If Caesar won, provided the Legion is still even around, which I heavily doubt because if they still were they would have already moved into a crippled NCR by now, although it's possible the 'Fall of Shady Sands' mentioned may not be due to the nuking but a part of a war against a victorious Legion which overextended itself and got wiped out only for Shady Sands to get destroyed shortly after the conflict when it got retaken. (Extremely unlikely)
Even the Legion won and is still against all odds holding on, I don't see New Vegas as being even remotely recognizable from what we see in the games after what they would do to it.
If House won, things would probably go into a downturn given House's reliance on selling water and electricity to the NCR and his tourist economy with them, although people will still come, and water is still a vital commodity House would have to take a lot of upkeep cost to keep them going, he probably will poach higher learners from the NCR to help fuel his initiative to reignite the technology sectors.
In other words, it would take tremendous wind out of House sail but wouldn't stop him entirely he probably would face a little unrest but would keep things together.
If Independent Free Vegas happened, things would be far more chaotic than House although still far less chaotic than if the NCR annexed the strip, there wouldn't be a power vacuum but without the central guiding hand of Mr House to keep stability things would be more hectic, if the Courier is still in charge of Yes Man then things might be somewhat alright but if he is dead or just vanished after the events of New Vegas leaving no power structure for the city then things can get very bad to the point the NCR might as well have been in charge for all the difference it makes with factions vying for control of Yes Man.
It's all a big question mark really.