I have the Champion 3100 gen plus a 13.5 btu AC. It does run it. However make sure most things are unplugged, it will run the fridge as well and the hot water tank plus radio at a low volume. But to start the AC I just make sure nothing is plugged in and the phones laptop etc are plugged in. I do plug the phones to charge once it's going. I also turn off the hot water. I pretty much turn off everything I can until it cools down a bit.
Well buy what you like I always say. I brought two Honda's 2000i eight years ago and they are still working great. I brought the parallel kit off of eBay that has a 30amp connection on the face plate. I made a extended fuel tank for my Honda's to run them as long as I like
I've had a Boliy generator for almost 5 years and until this year, ran it on average 8 hours a day for 1-2 week trips. Now that I have solar, the Boliy is run only an hour or so each night to cool camper and cook some microwave popcorn.
It is a true 3000 watt generator and is feature rich.