You can start and run the AC unit on a 20 amp circuit, but over time it will damage the air conditioner because of low power supply. It will also overheat the adapter and the receptacle, and those will be damaged too.
The specs for AC units say if the length of the wire is 25' or less it can be 12 gauge. Longer runs are required to be larger gauge wire, meeting the NEC. The 20 amp circuit in your house is 12 gauge, if it is on a 20 amp breaker. If it is on a 15 amp breaker is only on 14 gauge wire. You are adding more wire length with the power cord, exceeding the AC unit's specs. (heating up wire, burning receptacle, burning cord ends, damaging the air conditioner, maybe damaging the house wiring)
The issue is: the AC unit itself requires a little more than 20 amps, for milliseconds, just to start the unit, a little less amps when running. When you use any other outlet inside the trailer the total load exceeds 20 amps at times, (tripping breaker often).
Even if you do not connect anything else to receptacles, the converter will cycle on and off at times when the AC unit is starting, exceeding the 20 amp capacity. (tripping breakers, and damaging things)
To do what you are wanting, you need a 30 amp 120 volt dedicated circuit, with an outlet to match the cord on your trailer.
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Alan
2014 Silverado LTZ 1500 Crew Cab 5.3L maximum trailering package
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