I can tell you first hand that one eu2000 will not start the 11k AC. compressor. I tried this experiment about two weeks ago very briefly, and indeed, the AC does require a substantial amount of juice for start up. The AC and the generator just sort of choke.
You would need 2-2000's hooked up in parallel or one 3000. Do a search on parallel or honda and you willl come up with loads of info.
The 2000 is a great unit, and easy to schlepp around.
Sometimes I wish I were living in the stone age. Then I would know I'm the smartest person in the world.