> I believe most of those POS systems can operate in offline mode, in Europe at least.

I was able to pay "offline" for my groceries at corner store nearby when their terminal had really bad or no connection at all - and that did happen a lot. They were just gathering all payments and when the "computer guy" was around he'd upload these to the Internet. The only caveat was that for some reasons these payments would be stuck for more than a week on transactions list