Not debunked, but it's all theoretical and controversial, as I say nobody really knows. Many still reasonably suggest there'd be mass extinctions from a "minor" nuclear war. Some disagree.
Basically everyone agrees there'd be some form of globally damaging fallout. Whatever the case, I'm not that eager to find out, personally.
Does dissuading fascists from voting actually help? The more important part is convincing proles that voting is immaterial and they need to do other stuff to effect change. Whoever and however anyone votes, fascists will get into power.