Yup.
From the factory, there is no house battery on the B1500, at least there wasn't in 2000.
Unfortunately, there is no good place to put a battery. It needs to be vented and separated from the interior unless you use expensive sealed batteries.
The only place like that is the propane compartment, and even though there are electrical wires running through for the tail lights, people poo-poo the idea swapping one of the tanks for a house battery.
I think the newer ones have batteries now, but I'm not sure when that started.
The furnace is 12V. If you have 12V power when the camper is plugged into the truck, the furnace will run.
However, remember that you are drawing off your truck's starter battery!!! Do that too much and you will be STRANDED.
In my case, I usually have my enclosed trailer hooked up when I'm camping. My house batteries are in the trailer.