Will 20 amps run ONE air conditioner: YES (however read on)
IN fact if you check your breaker box you will likely find a 20 amp breaker there marked AC or A/C (Air Conditioner) so ti's a 20 amp device.
Mind draw 13-14 amps running.
However your Converter is also drawing power 1-10 amps depending on the size of the converter and condition of your batteries and thigns
The fridge draws 3-4 when cooling on A/C (force it to Gas if you can).
And make sure the water heater is either A: off or B: gas.
YOu can more or less ignore the contribution of modern flat screen TV's but older CRT's are close to the Fridge in power draw. 1-4 amps.