I tried using my Honda EU3000 on my 15k AC and it did NOT start. It tried, but it wouldn't kick on. We had nothing power hungry on and I was testing it just in case it got hot later. It was only 70 outside, but we were at an elevation of 8,000 ft. I have read that some people can use a 3000 for their 15k, but not us.
The recommended size is at least 3500 per the dometic chart. I'm looking at buying two Honda 2000's.
Hope this helps,