Can I enter the US on ESTA with a K1 in my passport?

[hobbit 10]

I've just gotten off the phone with one of consular officers and he's not positive that I could use the ESTA if I were already issued the K1 in my passport. However, he did say that they would be able to delay the interview until February as long as the consulate receives a notarized affidavit from both of us stating that we still intend to marry. It's either this, or just wing it- enter the US on the K1, marry in a few days, file the AOS/EAD/AP and hope it arrives before Feb. I honestly don't feel too good about postponing my interview date since you can only do it once.

The CO on the phone says that the visa is issued within 5 business days. We were thinking of me flying out in mid-November, though I'd like to push it sooner to early Nov since even a few days make a difference for the AP. I personally would like more time to plan the marriage ceremony and to combat jet lag.