Let's assume a nuclear exchange happens at some point during a war. There is a very high chance that this will cause an escalation leading to a nuclear apocalypse.
Since this result is presumably inevitable at increasing frequency, it's more like nukes prevented another major world war and stole a form of peace from the future, temporarily. That peace debt might be repaid with the end of everything.
let's assume the trees rise up and set fire to the ionosphere.
well whatever society is left will definitely be "peaceful" for at least a couple of decades.
https://en.wikipedia.org/wiki/Nuclear_close_calls