If it's limited to your country then the value of Bitcoin should remain fairly intact. A global catastrophe might really hammer the value of your Bitcoins (as well as other exchange mediums and moneys) because basic things like food and shelter would become very valuable relative to what the value was before the event. At least, that's what I think

So assuming my Bitcoins still have sufficient value that it would help me in my quest to shelter and provide for my family, I would:

Wouldn't be out of the woods yet, because if no business or individual in the area accepts Bitcoin for basic goods, then you still have essentially nothing to work with, but at least you now have a working phone, which even without the Bitcoin should help you going forward

On the other hand, if people and businesses in the area generally accept Bitcoin for goods and services your would be able to use the Bitcoin you have for your needs (assuming you have enough Bitcoin in that wallet of yours)

Overall I would be glad I stored wealth in Bitcoin rather than my native currency because it would take a lot more for you to get any money out of your bank account and into a foreign bank account (that you have to open first and seeing as you don't have anything with you like identification or a passport it could be extremely difficult). Some banks also require permission from the relevant reserve bank to make international payments and if your country is struck by such a catastrophe then maybe the reserve bank, if it's still there, will just deny any money transfers out of the country. Plus, your native currency is likely to also have taken a massive hit in terms of it's value because of the recent event so even if you get it to you then it would be worth a lot less wherever you are