err - I'm not sure doug, as you might guess i'm electrically challenged and shy away from currents and answers that may electrocute me or others. All I have a working knowledge of is driving Priuses and I'm a happy customer for that. I *think* when you plug in a simple inverter (you mean a socket plug into which you can plug in a standard household electrical plug?), it runs off the 12V battery, which is (probably) charged in the usual way. You need the car to be powered on to use the inverter, and the hybrid battery occasionally kicks on during charging, so there might be a charging connection, then again maybe not.
I get in and it works, and when it stops working I'll probably park it in the backyard and grow blackberries over it.