Alright guys so here's the report. Even a "bought outright" "payed in full" phone ordered online from ATT seems to come locked. I don't have another carrier's SIM to try but I don't have any band options under "Settings"-> "Cellular" (which people online say is a way to see if it's unlocked. If anyone knows another way to check for locked/unlocked status, I'll be glad to try it out.
Now, I unboxed the phone and immediately removed the SIM it came with (before powering it on) If you currently have a Nano SIM, you can just throw it in the slot and turn it on, it should be good to go. My old LG phone had an older Micro SIM so after removing the Nano SIM it came with, I went to the ATT store and had them move my number from old pre-paid (contract-less ATT) account to a brand new Nano SIM. I put the new SIM in the phone and bam it worked immediately in the ATT network with no problems.
Then, I went home and called ATT Customer Service at 800-331-0500. I told the agent that, "I ordered new ATT phone service online but decided I didn't want it and would like to cancel it before ever activating it." I gave her the number that the original order assigned me. I then explained that I would be keeping the phone but wanted to make sure the service was canceled and wasn't billed. She did ask if I was going to be using the phone on another account to which I replied yes and already had it activated. She did Not ask any more questions regarding the phone. The only thing she needed was the security PIN that you either create when ordering the service online, or it may have had you create the PIN when you first called Customer Service. It took about 8 minutes tops. She informed me that the service was canceled and that I would receive a paper bill next month in the amount of $0.00 simply for account records. I verified that there is no activation fee since I didn't activate a new phone. I submitted an Unlock Request here
https://www.att.com/deviceunlock/#/ although I have a feeling I'll have to wait at least 14-days before I get that approved. I am curious though since I have a pre-paid account if they will make me wait the 6 months to unlock it. But, if you're buying the ATT phone for future resale, and wanting to take it to another carrier, only the 14-day unlock policy applies.
There you go folks. ATT model A1633 model iPhone 6S bought outright without having ATT Post-Paid service.