Question about diesel engine heater (not glow plugs)

I cannot find this anywhere in the owner's manual. I have a console switch to turn on the engine heater for very cold weather. I would use it for several hours before trying to start the engine, but I would only use it if it runs directly off the ac connection and not off the house battery pack. I know that, if I'm plugged up, the batteries continue to charge but whether or not the charge would keep up with the load, I don't know.

I have a 2006 Phaeton with a Cat 350 hp engine.