It takes up a good chunk of floor space: I have a 7,000BTU (EDIT: 8500BTU) portable AC that stands on wheels and vents out through a window with a hose. My 2000w Inverter generator can run it, but, can NOT start it up when it is in ECO mode.
I think you can get those in smaller BTU models that a 2000w would run and start in ECO mode... I use mine at the storage lot on hot days along with my gen if I need to do work inside and it is perfect for my need. It would work if I were boondocking and willing to run my generator with eco mode turned off. But - It takes up a fair amount of room as stated.
EDIT 2: If I read your reply to Charlie right this solution might work if you were willing to give up the floor space and make a more secure way for it to vent to the outside. A buddy of mine used plexiglass with a hole cut in it for the hose because the supplied window adapter would not securely fit in the window he wanted to use.