Typically not. But the best way to confirm would be to use a volt meter and test.
Ours did not so we installed a Trik-L-Start so that it gets charged on shore and genset power.
Your profile does not say what class c motorhome you have but if you have a battery management system installed, I believe the chassis battery should be being charged after your house batteries are at full capacity
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Roy(Opa) and Hilda(Oma)
Bowling Green, OH
2017 Seneca 37TS
2010 Toyota Tundra toad
Does it work in 'reverse' as well? The chassis battery is charged and then the house via the alternator?
Yes, the alternator will charge both chassis and house...that is a factory setup. It just doesn't do the other way around and use the converter to charge the chassis battery...unless you install this Trik-L-Start.
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2018 Greyhawk 29MVP
2018 Jeep 4 Door Rubicon Recon
Retired and Under New Management (See Spouse For Details)