Our old 2000 Four Winds didn't charge the chassis from the house converter/charger, so when we got our new 2016 Sunseeker, we were pleasantly surprised when the modern BIM took care of the chassis battery as well.
With the unit plugged full time in over the first winter, I've had a little liquid bubbling over on the chassis battery in the past and had some corrosion in the engine compartment at the battery base to clear up that spring. Now I leave the unit plugged in for a few days, then off for a couple-three weeks.
My monthly maintenance schedules over the winter include starting the MH engine & running for a period of time, ideally with a quick run to town & back. I also start the generator & load it for an hour or so with either the roof air or a portable heater. The engine start is around the first of the month, and the generator start is around the 15th. This way both exercise & contribute to the maintaining of the batteries, if only for a short time.
Formerly: 2000 Four Winds 26Q/Ford, '96 Kit Sportsmaster 22' 5th wheel, '91 Sunlite truck camper, Wildernest flip-top canopy