Yes. The frig needs 12 volts for th e controller board to switch between gas and 110 volts. If the friig doesn't get 12 volts, it doesn't work.
When you are on shore power, the frig gets its 12 volts from the converter (a 12 volt power supply /battery charger)
ALSO - You would probably want to turn the battery switch ON anytime you are on shore power, otherwise the coach battery will not charge.
2001 Coachmen Mirada (Ford F53 6.8L V10) - Toad 2001 Civic
It won't do MACH 2, but I can get a sandwich and take a pee.