I run our Axis' A/C all the time on our house 15A plugs.
The biggest issue is startup current. When the compressor kicks on is when it draws the most current. In my case if the circuit I have it plugged into has anything else running I'll trip the breaker. If I keep everything off that circuit it has no problems.
I also used to run our 5th wheel's A/C on the same 15A plug. Had that guy over 10 years and never had an A/C issue with it (also ran the A/C on the two other campers we had before that on the same plug).
I don't see how you can burn up the compressor--unless there are some problems if the compressor suddenly shuts off right during startup (which is what happens when the breaker trips at max current) but, again, I've never had a problem.