I'm pretty sure offline is supported, unfortunately in the UK despite this some train services have online-only chip+PIN machines in their buffet car, forcing you to wait until they get good signal to pay for your food!
It's visible to the customer as a much faster process -- you can remove your card around a second after you enter your PIN, instead of waiting 4-5 seconds for authorization.
I think normally cards get a limit of offline transactions before they have to do an online one. I think it's about 7 or so before an online transaction is "forced".
This seems about the correct number. It is similar to how the contactless support works. You are forced to use the traditional Chip and Pin method occasionally. It seemed to be about 5 transactions for contactless initially but I feel they have increased the limit now.
It's visible to the customer as a much faster process -- you can remove your card around a second after you enter your PIN, instead of waiting 4-5 seconds for authorization.