first of all i doubt that there will be such war as i think people are evolved enough to not do that kind of stuff any more and no one will want for it to happen
though if it will happen nothing will survive it and if even bitcoin would survive it there wouldnt be anyone to use it, so i guess the answer would be that it wont survive it at all
That's right, no one wins in a war...Besides it costs a lot of money..But I don't think that if it happens bitcoin will be gone too..There are still part of the earth where war haven't escalate yet and probably there are still miners in that place and internet too, if it is still present, then bitcoin is still alive and most probably be used widely after the war...