Question about upgrading via AT&T Next

I'm planning on upgrading to an iPhone 6S Plus (64GB) very soon. I was thinking of ordering online and getting the phone in the mail and I was planning on this being a gift (to future me). If I order the phone now and I don't use it until around the 28th of December, will I be billed for both the new iPhone & my current 5S?

More info: My 5S is 16GB under a 2yr contract that expires on the 28th and the phone currently costs $25/month.

TL;DR: Upgrading iPhone 5S to 6S Plus. Will I be billed for the 6S Plus & the 5S if I only use the 6S Plus 3 days out of the month of December?