If the only basis for Bitcoin to survive a world war only the internet then, I am 100% Bitcoin network will survive. It may have to stop during the war but when it is over, the network will go back alive since internet will surely reestablish after the war. Though I am sure lots of Bitcoin will have lost its owner and private key.
You're right, if there is a bunch of Bitcoin holders that died within the World War then there would be a smaller supply of Bitcoin available within the world. It's pretty messed up though it is what it is. If Bitcoin has a strong network or if someone implements Bitcoin on a meshnet then the people that use Bitcoin when/if that World War situation starts they will have a chance of using Bitcoin later when the War is pretty much over.