I purchased a nice 2400 Yamaha generator to run my 1600 btu marine air unit and it would not start it - you may however be able to have a modification to the marine air unit to help it draw less starting power - one can look into that
Find out the size of your ac unit - if a 1600 BTU it will most likely not start up with a 2200 generator - it is the start up process on a marine a/c -heat unit that draws the most power