The inverter will never run or help the air cond run it wiil just comlicate the power that you get to every thing on your camper , it may work just fine the way it is depending on your needs
I my case I use a sat tv box , dishnet and they are so finiky the slightest power fluctuation and they restart , which takes a while and is a pain in the rear , so I dont run the air cond that way, I even have my micro fed thru the inverter , which transfers to ac when gen is running , and directly from ac , Both romexs go to one duplex outlet thats split (seperated) and I can plug into either one to suit the situation , that way I can also run the micro and air at the same time if I have the inverter on and am running the gen. by turning the breaker that feeds the inverter ac curent off