If World War 3 will be ignited, I will worry more about the safety of my family and other people. I won't care for anything but its the survival of my family. But in regards to Bitcoin, reports have shown that the negative effects of war on economy include increased public debt, increased levels of taxation and inflation. This will affect again the volatility of Bitcoin. It can be more expensive vice versa. The problem is that the effects of military spending are not productive when compared to the economic needs of these other areas. So, I think it won't happen 
Just think about what the third world war means. It can generally bring destruction to every country and this means the lack of electricity and even the Internet. Thus, bitcoin can and will be expensive to build, but the demand will be in other values, material.