I mean, the main reason that the Soviet Union was reluctant to use nuclear weaponry is that during much of the Cold War they were at a huge numerical disadvantage to the United States (there was not true "parity" until the 1970s-1980s), and even when they weren't, the numbers of weapons were so massive that total destruction of them (and much else) was inevitable.

I have never seen anything that suggested atheism had anything to do with their perception. I am not really sure how one would establish such an argument anyway. There is certainly no body of evidence that I have heard of us where one sees Politburo leaders saying things like, "But Comrade Khrushchev, the lack of an afterlife must surely constrain us in our otherwise great plans to nuke the United States!" It is sort of a silly thing to imagine.

The most interesting question is, does belief in an afterlife make you think that nation-destruction would be acceptable? There is some evidence that Reagan had millennarian inclinations (e.g., believed that judgment day was around the corner, that nuclear weapons might be involved in it), but other than that I can't think of any leaders where you could make much of a case study in that (and in Reagan's case, he had more complicated feelings about the weapons than just that).

As a follow up, I heard a different explanation - that, being good Marxists and so believing that capitalism was ultimately doomed and the eventual victory of communism inevitable, the Soviet leadership saw no need to use nuclear weapons since things were going to go their way in the long run. Anything to back that up?