The bitcoin world is running by people. No people, no bitcoin. Therefore, if the disaster hit the earth, people would be gone, thus so would the bitcoin. Added to that statement, what do you mean by big wars? Nuclear wars? If so, people would cease to exist. So no bitcoin.
So, basically, whatever happens to the earth will decide whether the users of bitcoin will still run it or not.
That is just the plain case here. When we are talking about a global disaster, then obviously everyone on earth has been cleared out. In that case, there is no fiat, there is no asset, there is no cryptocurrency and there is even no internet. More like a total black out.
Whatever happens to bitcoin will happen to every other thing else. Moreover, who is even going to buy your bitcoin or anything else in such scenario when everyone is struggling to survive ?