Unless there was a cataclysm that destroyed our entire technological structure, I don't think that a world war could have any significant effect. While it's possible to continue mining cryptocurrencies and continue using mobile phones or personal computers to send or receive them through the internet, I think that everything would continue more or less the same. Regarding the price, which is what many people care more than anything, you can think that a world war would cause an economic depression and a lot of uncertainty, this could make many people think of cryptocurrency as a refuge, it's a possibility, but I would not bet completely for it either.