Assuming this world war would be on a scale larger than the previous, all economies would be affected, including cryptocurrency. It wouldn't suffer as much as fiat though. I think immediate impacts would be some fiat immediately devalued as opposing factions stop recognizing each other's national currencies. Others would be vulnerable to hyperinflation.
I imagine Bitcoin itself will soar in value, but there will probably be wild variations across exchanges, with many possibly choosing to abstain from trading with fiat. If anything, we might see an uptake in crypto adoption as governments rush to hedge and protect their assets.
Mining rigs might also be military targets. Can easily see this happening. Power rationing would mean shutting down all non-essential use of electricity, so industrial miners can say bye-bye, probably even have their hardware conscripted for technological warfare.
It will certainly affect the price. Imagine if there is a world war goin on, do you think people will still be infront of their computer and make crypto trading? If world war will be going on, crypto prices will become zero because probably, countries will shut down their internets.
Nodes will find a way around that. Blockstream's satellite network comes to mind.