No, because giving money is only a part of the transaction.
> Do stores really need to be connected to the internet all the time?
Yes, they need to record transactions (in some cases live for tax purposes), update inventory, and in the case of a pharmacy also check medical files (if such a feature exists in the country in question), verify insurance information, check usage details on the specific drug, etc etc.
Some of those could be batched offline and verified when the connection is back up, but others can't.