Actually it depends on whether you have an isolator or a separator. In the case of the former - no, in the case of the latter - yes. We have a separator on our 2008 Chevy 190V and have replaced it once because of it being faulty - not charging the coach batteries while driving. Both coach and chassis batteries are now charged when driving and again on shore power. There is a caveat and that has to do with the charged state of the "local" battery - chassis battery when driving and coach battery on shore power. I have used a "clamp" multi-meter to check this out for my own satisfaction.
"Drive with Care, Life has no Spare!"
2008 Roadtrek C190V 6.0L Hella Fog, Nighthawk Driving, Halogen Reverse Lights, Fiamma Air Horn, Firestone Air Bags, Custom Bed & Mattress, Custom O/Head Tray. website www.sen-f.ca