It could survive, just send a usb with your transaction to every node through the mail. Simple.
It would be very easy to double spend your coins doing this. The various nodes would also not have a way to communicate with each other.
Yeah how does the block chain update without a network?
TELEGRAMS! Or morse code, sent to a (sadly) centralised station, or individual nodes which update a larger ledger. That could possibly work, but it would require a lot of stuff to be set up.
EDIT: Accidentally hit post before completion.