No, not necessarily.

Amp-hours tells you how much energy is in the battery, the amps tells you how quickly that energy can be delivered (For the most part, for a fixed voltage).

Your suspicion is well founded, because the Amp-hour doesn't tell the story on the batteries wattage capability.

Car batteries post their peak amperage because that is important when starting a vehicle. For your purposes, you'll want to find a deep cycle battery. Completely discharging a car battery pretty much ruins it. Deep cycle batteries are designed to be fully discharged, and those are rated such that they can deliver the full current pretty much until they are just about empty. 

You may be able to find a suitable battery, depending on how long you are going to run your microwave. A decent 20+ amp rated deep cycle should still be able to unload 150 amps for a minute or two. Don't run the battery full blast non-stop though, it will overheat. Shop around for batteries for boats, RVs, etc to find good batteries.