i can run my 1 ton ac on a 2.5kva chinese generator running on gas... probably very similar to yours..
the ac will run fine if no other loads... other wise it will run to 5amp, after which it will put much load on the generator..
my ac comes with a automatic circuit breaker. it trips if volatage gets too low.
so when ac puts too much load on generator, the breaker trips, instead of the generator. 30 seconds after volatge is normal the breaker starts again and ac works.
this normally happens when its really hot. when the room gets cooler this issue disappears...
i would rate running the ac on generator as smooth... its a big plus if you have the automatic circuit breaker.