I am pretty much sure that a war between superpowers (conventional) would end up nuclear, no matter what. Either in Fallout franchise, or in our world.
Think about it: what does the losing side have to lose?
They already lost the war. What is likely to happen for the government that authorised the war is some sort of war trial and death penalty (like in Nurnberg).
In the mind of people who are drunk with power and ready to throw the youth of their nation to needlessly & pointlessly die for their own lust of what they perceieve as power, what is worse than being stripped of power and, shortly after, life?
I'm pretty sure that it's mostly ego that makes the people "up there" do the crazy shit they do. And being publicly hanged after being called a failed criminal - well, that's exactly on the opposite part of the spectrum of stroking one's ego.
I'm pretty sure that, under such cirmcumstance, China would have nuked US in the world of Fallout, and that i.e. Russia would nuke US in real world.
Just look at the Enclave. Those presidents, kings and rulers always end up surviving and keep enjoying a decent and comfortable lifespan. Do you think the same stuff wouldn't happen IRL? pretty sure a guy like Putin would rather have 20-30 years more in a bunker, than 2-3 weeks before getting hanged over war crimes he's going to get accused of.
Nuclear war is inevitable should nuclear-capable countries go to full scale war.
This is why, in Fallout franchise, the "could have been prevented" thing is a no-no, it ended the way it had to.