Bill,
It would help everybody that wants to answer if you gave more specific information about the coach. Your profile list it as a 27' Jamboree on an E350 Chassis (460). The 460 makes it '97 or older, and that does give us much to go on here. It is old, but not vintage, classic or antique. That means that a lot may have happened since it was manufactured.
Unless someone added the device, I very much doubt that the chassis (main engine) battery is maintained by shore power.
The converter charger, if it is original is most likely not a modern three or four stage. As it probably is not, leaving the coach on shore power indefinitely is very likely to hurt your house bank.
That is all anybody can say with model numbers.
Matt