This is a rediculous idea. Again, nuclear power industry accidents across all of the history of the world do not exceed the amount of radioactive material that is launched into the atmostphere by the worlds coal plants in a single year, and we have been burning coal for almost 200 years, and seriously powering industry with it for over 100 years. Modern nuke plants don't really 'blow', and even if 100 of them had leakage accidents similar to what happened in Japan (very, very unlikely) we still wouldn't exceed what humanity has already dosed our environment with over the past 100+ years. That plant had a quadruple redundant emergency cooling system, which we now know isn't quite good enough for a 1:10K year tsumami wave. It's certainly more than enough for a global economic breakdown,
Dream on! (your ridiculous dreams).
Fukushima blew out a significant part of its inventory. In case of a black out of the whole power grid, which is a question of when but not of if (sun storm, economic collapse and panic/revolution etc.), it would have blown out its inventory totally, and so would have all the other reactors. Power grids become more and more fragile to maintain the 50 Hertz, totally depending on the computerised, hypercollectivised communication system.
Societies collapse, because societies are problem solving societies (Tainter). Each solved problem increases the complexity in the system, and increased complexity generates diminishing returns until the end (bifurcation point), when additional investion in additional complexity generates negative returns. Forget at least the northern part of this planet if this society will not end the nuclear industry.
Probably it won't, because society means collective stupidity, which until today always ended collapsing. This society will also end abruptly in a worldwide, globalised panic with worldwide bank 'holidays' and nobody will go to work anymore; not to the banks and not to cool the nuclear reactors. Nuclear reactors need each other to cool them, but after a black out you'll have to cool all of them. The collective stupidity will not be able to do this.