The main issue is the electricity and the internet service, because Bitcoin is dependent in this two elements to survive, however i don't think that all the humanity will die even if WW III happen because it will finish with a gainer anyway
If the superpowers start nuking each other, then survival is not a question anymore. We will all be dead by then and bitcoin, even if it survives will be useless. In case of world war, survival is utmost importance, not money or digital currency. Water, food and medicine will be the most important things.