Bummer - I checked the manual, and sure enough, both power points (the 110 VAC and the other one) run down the 12V. The 110V has a 150W capacity, and has no juice unless the ignition is on. The other one is live all the time, and can handle up to a 180W load, but we're advised not to leave things plugged in when the car's not running, lest we run down the battery.
Seems like a waste to me, all those volts/watts/whatever just sitting there, and I can't even use them to chill my brewski.