Since last year I had paid off my iPhone in advance of the release of the 6s Plus I was unsure this time around just how this whole process works, so went over to the local AT&T store and learned the following:
1) One can pay off the phone in full which then completes the current NEXT plan and frees the customer up to preorder or to purchase the new iPhone at the Apple Store, AT&T or any retailer which has the iPhone 7 available on Launch Day.
2) One can pay just the monthly payment amount needed to ensure eligibility if the usual payment date falls beyond the date of Launch Day, which in my case it is -- September 25th. This is done online at the time of preorder or online/in-store at the time of purchase and ensures that the NEXT account still remains associated with both the current and the new iPhones. With preorders, one then can ship the older iPhone back to AT&T when the new one has been received and is activated.
This cannot be done at the Apple Store or through the Apple website, it has to be done through AT&T. (That was the part about which I was uncertain.)
Hope this answers questions others might have had, too, about the process!