How would Bitcoin usage be affected within a country that severed its Internet connection? Clearly this system depends upon data exchange.  What happens if national authorities in one or more countries decide there exists a "national emergency", "requiring" the shutdown of the internet in those nations?  How then does this system work?  Will commerce aboard this platform come to a halt, or is there a redundant communications method?
A government that shuts down its Internet to civilians is a government in crisis

The economic cost of shutting down all government regulated Internet connections within a developed country is enornmous. It is extremely unlikely that a first or second world government would take this step simply to block Bitcoin transactions. It may be that if Bitcoin rises to become an ISO recognised currency traded by governments the decision is made in order to somehow preserve sovereign wealth in the native currency that is now under threat from Bitcoin, but that is a long way off from today and would ultimately prove futile. It would also show very poor financial planning on behalf of the nation since they can simply continue their mandate that all taxes and fines must be paid in legal tender forcing a conversion out of Bitcoin to their native currency.

The question of how Bitcoin could respond to such a switch off is similar to how the Internet itself would route around the problem. There are a multitude of ways that ad hoc networks can be established. Bitcoin has been shown to be at least as resilient as the Internet in terms of the myriad of ways that transactions can be made to reach an Internet connected node. For example, Bitcoin transactions have been transmitted over HAM radio, NFC and Bluetooth. There are many alternative digital networks that can serve as backup routes to the wider Internet.

Even in the total absence of electricity, the Bitcoin network can survive through physical bitcoins. So long as trust is maintained in the security seal protecting the private key it is only necessary to conduct occasional verification checks that the amount displayed on the token represents the amount accessed by the key. Simplified pricing schemes (to allow accurate change) would enable invisible private key based trading. An occasional radio broadcast to co-ordinate the current bitcoin value against other currencies in use would be sufficient to allow merchants to price their goods accordingly.

Remember that in times of trouble people will seek to use whatever they can to get by. If bitcoins are perceived by most as being the best way to conduct trade as, say, the dollar enters hyperinflation, then they will use them. If something else provides a more stable medium that is more appropriate to their circumstances they will use that. However, Bitcoin is by far the most flexible form of money ever invented so it seems likely that it will survive better than others.