In a crisis significant and widespread enough to crash the dollar or any other government-backed currency you'd like to pick on, it seems likely that there would also be significant disruption to electrical and communication networks, which does not suggest BitCoin is a great thing to hold for that situation.
(a similar point is often raised against gold, in that a post-economic-apocalypse world would not immediately have the infrastructure to verify claims like "this is one ounce of pure gold", meaning gold's utility as a medium of exchange would not be as high as suspected by people who buy it to hedge against such apocalypses)