As only a GUESS, this sounds do-able. To second-guess my guess, I understand Yammie 2400 to be a true 2400 continuous with still higher surge, while Honda 2000 is realistically more like 1600 continuous.
What I'd like to add is this - From other threads, I've learned that at least some RV builders order their A/C with "hard start kits" because they believe the RV (usually a Class C or Truck Camper) will have a Generator and a Generator will need help. That can leave Travel Trailers out in the cold (well, er, Heat, I suppose...) since the premise is they don't come with a generator so they just must be getting plugged into shore tie. Then you guys come along and want to run with a portable generator. That might mean the A/C a trailer comes with, let alone one you might buy, will not have the Kit. The Coleman (rvcomfort.com) site should have the Parts List and Wiring Diagram for the A/C you're considering. Parts List'll show the Start Relay and Start Capacitor as if they're installed even if they are not. Wiring Diagram will show two dotted lines to the Compressor Run Capacitor, dotted because it's an Option that may not actually be there.
My GUESS stands: 2400 Generator and 13500 A/C With Start Kit should run, but it'll be Load Shedding. A/C off to run Microwave, etc. Our Coleman Mach 15000 needs to be OFF for Load Shedding about 5 minutes before it'll re-start. That's at least under low campground voltage situations.
