Probably yes. I have heard that when the compressor kicks in on your roof air it has a surge draw of 18amps. So if you have a 20 amp circuit breaker, you can't have much else running at the same time. I run one OK at my son's house a lot without any problem, except on his electric bill!
I'm installing 3 additional outlets in my motor home...
2 120volt 30 amp RV type (These are pigtail type outlets, 9 bucks each)
1 240 volt 4 wire twist lock 30 amp connector
Box, wire, clamps, wire nuts and 2 double breakers (30/15) 12 feet of 10-4 stranded wire
Total, not counting labor (I will do it myself, fully qualified) is about 100 bucks so far
Heavy guage wire (10 ga for 30 amps) is pricey, however it's worth it.
12 ga (20 amps) is much less expensive... but use a 20 amp breaker
Normal use, one of the 30 amp outlets will feed a special cord I made up for my old trailer, this originally was the power system for the old trailer, now it will be the power system for the picnic table,,, I mean, I just did nto wish to scrap the cord and outlets
Emergency use... If I don't need AC (IE: Cool night, just need furnance) in a blackout situtation I can power at least two other campers (30 amp each, though in truth 30 amp per leg is all the generator does) IF I can get by on one AC, then one other camper (The outlets will be labelet as to which one is which AC
Emergency use at home...... House has a 30 amp 240 volt inlet matching the outlet i"m putting in the MH
If you have a 20amp circuit you should be fine to run the AC. You probably can run the refer as well. Don't try a microwave or coffee pot. If the compressor comes on at the same time it most likely will pop the breaker.
When we owned a house I installed a 30amp circuit where I parked the coach. Then I could run everything but two AC units.
Did you note whether the house circuit was a 20A breaker or a 15 Amp? Or check to see what else in the house shares that same circuit? The a/c will definitely run on a 20A and probably run on a 15A, but on 15A you can't have other stuff powered in the RV. And whether 15 or 20 amp, there should be nothing else in the house powered on that same circuit - the Rv will need every bit of ot! or