Card payments, including contactless payments, can be done offline. However the card has to be configured by the bank to allow this, which I guess some do not.
It's a very specific notion of "done" - you can record an offline authorization event; so the customer-visible part is done, but the actual payment is not.
The merchant is not going to have any access to that money whatsoever until/unless connectivity is restored. They can't pay their suppliers or employees with that money while they're offline.
It's pretty much the digital equivalent of scribbling "Bob authorised to pay me $12.34" on a notebook that you're going to bring to the bank afterwards.
Even if the transaction is online, you don't see the money in your bank account straight away. It takes a few days for card payments to settle, and usually the payment processor will have a predefined schedule as to when you get paid. The context of my comment was on the payment terminal being offline for a day or two.
Emphasis on "can". The system at the point of sale that processes the card has to support that as well, quite a few of them don't and rely on some sort of centralized infrastructure to function, at least around here in Germany.
The merchant is not going to have any access to that money whatsoever until/unless connectivity is restored. They can't pay their suppliers or employees with that money while they're offline.
It's pretty much the digital equivalent of scribbling "Bob authorised to pay me $12.34" on a notebook that you're going to bring to the bank afterwards.