You can put a volt meter on the chassis battery and the coach batteries while at rest , should read about 12.6 volts.
Then plug in the MH to shore power and do the same voltage test , should then read about 13.4v or higher.
On some MH's, the MH converter will charge all the batteries, it will depend on how its wired. An isolator solenoid (which acts as a one-way electric gate) should protect your chassis battery from draining while boondocking etc. but that gate would open up to allow your converter to charge all the batteries.
If not, then you need to take measures to monitor the batteries not being charged.
You may have a
BIRD or a derivative of it my Tioga has one and I know of many RVs that have them,It will charge thru the Continuous Duty Solenoid Relay as mine does. It may be located in your battery bay as mine is.
Click For Full-Size Image.
It senses voltage on the coach and chassis batteries and charges the one that needs it most,when it is at full charge it will return to the normal function.
2006 TIOGA 26Q CHEVY 6.0 WORKHORSE VORTECFormer El Monte RV RentalRetired Teamster Local 692Buying A Rental Class C