I just picked up a Yamaha e2400ishc and it does start/run the 13,500btu A/C unit in my TT. While the A/C is running I'm drawing about 14A total with a couple of those amps draw from the TT when idle (microwave light/timer, stereo, Co2 detector, etc.), so there isn't a lot left to run anything else while the A/C unit is running. I did turn all the TT lights, the frig and stereo on while the A/C was running and the generator didn't go into overload mode.
2012 KZ Spree Escape E204S
2007 Chevy Silverado 1500 4.8L, 3.23