There's no particular reason to believe this is going to make global thermonuclear war any less likely. Russia and United States aren't particularly likely to start a global thermonuclear warfare anytime soon, and in longer perspective any major developed country, if it wanted, could build nuclear arsenals sufficient to make a continent uninhabitable within a few years.

There's also this argument that mutually assured destruction was somehow stabilizing and preventing nuclear warfare - the only use of nuclear weapons so far happened when the other side had no way to retaliate. I'm quite neutral on this - I'm unwilling to say that nuclear arms reductions either increase or decrease risk of global war (which will eventually turn nuclear or otherwise very nasty).