If you go back to Generator School 101...you will note that volts x amps= watts. That number shouldn't exceed the rated output (in watts) of the generator. Rated output is the amount that the genset can sustainably produce. Max output is the amount that the genset can deliver for a short period and deals with starting current (aka power factor). That is how marketing departments usually derive their model numbers for the generator is max output.
On electric motors, especially starting under load you can just about bet that pwr factor will be 1 1/2X, even though momentarily. The bigger the electric motor or starting load( like a pump) the greater the power factor will be. You are probably not going to be into the 2 or 3 range in power factors in your application, that would be in air compressors or such.
ie. I have a 13.5K Btu AC and my Honda 3000i Handi will do it. but, I can't tell by the way the genset sounds that it is giving it's all. Crunch your numbers 120V x (x) amps= W, W X 1.5= starting wattage. This calculation, should give you a better idea if your prospective generator is going to do or die. You will be able to tell by the way the AC starts on the generator vs. the shore power( it will take longer) you may see an overload indicator on the genset or pop the breaker. I will tell you repeated popping of any breaker is not cool and over repeated situations will compoimise the the breaker's ability to control overload