Yes, you can run the AC with a generator. I'm not sure what you mean by "Factory AC", but a Honda or other make 2000 watt sine wave generator will run most 120 volt ac air conditioners.
A small RV roof type or window type domestic AC unit can be run with a 1000 watt unit of the same generator type, but be sure the AC and generator match up before buying the generator.
AC units that use seawater for cooling are generally not as favored as the other types as the water pumps, plumbing, and through hulls are prone to fouling, especially in saltwater, and when a boat is moored rather than dry sailed (trailered).
There are several ways to mount the generator on the boat, depending on which model CD you have.
Joe. :teeth :thup