Q: Does Apple Pay support offline payment?

What do you mean by "offline payment"?

Apple Pay relies on NFC.  You do not need WiFi or cellular data to perform a transaction.

A Credit transaction in a Retail environment is an offline transaction, even as though their are online elements occurring at the Point-of-Sale.

If you are envisioning sitting down offline on your PC or Mac and setting-up a bunch of Payments using Apple Pay ...forget it. 

No, it doesnt require Internet to use Apple Pay! It works the same as your credit card!