depends on what your surge wattage is at start up from the ac motor, and then your running wattage, when running constantly. if start up wattage is 2200 or more watts, then no. example if I had an air conditioner, and the surge start up was 1500 watts. I only have a 1300 watt surge generator with 1000 watt continuous output, constantly, when running, then no. 2000 watts wont run a 2000 watt ac unit, not for long wont even start it up.anyways. lol
also then amperage comes into play with you. you could piggyback a smaller generator to your 2000 watter to boost it, you don't need another whole 2000 watt generator ,you don't need 4000 watts to run yer ac. ?????? get a window ac unit, save yerself money , hassle, and time, and fuel. run it off of generator at half to a 1/4 of what you are now. no ac unit in 2017 should even take 2000 watts to run, or start, unless you got a 50 ft camper.????
you could even try to piggy back from an inverter to it, from solar batteries.!
give you that extra watt boost you need, its not much you need to boost it to start up. just hook it up a 750 to 1000 watt inverter my old camper I ran 2/ 5 watt cfl's, 2 of them, my tv, my computer desktop, charged my phones and tablet, my outside light, all day and night 24/7 for 4 days, off of 45 watt solar panels, and group 29 100 amphr battery w/20 amphr reserve. battery never fell below 11.4 vdc when there was no sun. that's when charge controller kicked in. really 2/ 2000 watt generators for 1 ac unit? I doubt that seriously, to me.
thanks mike