Not necessarily. The issue is that we don't know what a modern nuclear bomb does to a city and n=2 (where only one was a direct hit) is a terrible dataset to extrapolate from. It all depends on if cities form firestorms if hit with a nuclear bomb. Atmospheric modeling of firestorms from forest fires is unreliable; there are hundreds of thousands of data points of forest fires and very few on nuclear bombs.

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.