Yes, it will power my 15k AC in Arizona.
I bought mine from Costco a few weeks ago. It too was $699. I sold my 2000i for what I paid within a day of listing it. The Honda would not power my AC. Best thing about Costco is I can always return it for a full refund if anything goes wrong with it.
With the Cabellas version above - the one drawback that I didn't like is the accessory setup is the positive and negative leads type of connection. With the one at Costco (slightly different part number and black), it has a cigarette type of connection for accessories.
2014 Jayco Jayflight 32BHDS
2015 Ford F250 Lariat 4x4 Crew Cab 6.7L Powerstroke