Does Apple Pay work without data or internet?

You do not need any type of internet connection, be it cell data or Wifi to use Apple Pay in stores.

Apple Pay in stores uses the NFC chip (Near Field Communications) to transfer the payment information to the store's terminal. There is no internet connection required.

Well, Apple Pay will work on an Apple Watch Series 2 even if the phone is out of range.

How to use your Apple Watch without your iPhone nearby - Apple Support

So, it seems reasonable to me that you could use Apple Pay on the iPhone without a data connection.

bsallis wrote:

Can you pay at a retailer with Apple pay when your cellular data is off on your device? What about if it's in airplane mode?

Apple Pay - Apple

I would assume you would need some sort of data or wifi to use apple pay.