No - it will not power the AC. It will power as a 15 amp provider (30Amp to 15Amp - 110 plug) which will keep your battery charger going and power fridge, lights, Tv.
If you want to run a full 30Amp to power the AC, you'll need a 2000 and a 2000i with the companion connect kit. (preferred due to size and portability) or you can get a Honda 3000
2015 25' Eddie Bauer
2015 F250 TV-Petrol