Do Trucks Have Power Outlets?

Definitely so. The APU runs AC, heat, or just fan, As well as keeping the batteries charged. I don't believe it sends any juice directly to the inverter though. Now as long as I don't turn the apu completely off it will cycle on and off to tend the batteries so I shouldn't have any issues with coming back from home time and finding the truck dead.

Unfortunately, I do NOT have shore power. I suppose it isn't really necessary but it would be nice to have like in an RV so if I happened to bobtail to an RV park I could avoid having the apu run and annoy people at night.