I assume you are talking about the Honda 3000eui, which is the inverter model raher than a mechanical a/c generator.
Yes, the 3000i will generally run an a/c and anything else you need to power. It may depend, though, on what micro you have. The convection oven types can consume a lot of power when in oven mode - up to 20A for some of them. Even then its probably OK, but you might trip a breaker once in awile if the a/c compressor cycles on just as the micro load also peaks.
A typical micro draws around 1000-1500 watts (8-13 amps) and uses about the same power as your a/c. But micros usually don't run along time (2-5 minute sis typical) and the a/c draws max power only when the compressor first cycles on, so there is usually enough power for both. A 4000 watt would eliminate the marginal times, though, an dleave some extra for tv, converter/charger, etc.
Make sure you can actually use the full 3000 watts with your trailer hook-up. A trailer with a 30A power cord can only plug to a 120VAC outlet and many generators only deliver full power to a single outlet via the 240V receptacle. If you have a 50A power cord on your rig, it can plug to a 240V outlet (with a suitable adapter).
