I called my local Apple Store and they're not 100% sure either. The person I spoke to said their manager was trying to confirm it. They said on one hand, the phones sold through the Upgrade Program are unlocked so you should be able to pop in any nano-SIM card and go. On the other hand, they found that there was a requirement to activate each phone sold through one of the four major carriers and that would not be possible with a AT&T GoPhone prepaid account.
But he did say that I could sign up for service through a carrier when I came in to pick up the phone at the Apple Store, so it looks like that's what I need to do. He said the Space Gray 6S 128GB is a pretty sought-after model so it would be a while before I could get it otherwise.