So, yes, the fridge needs 12V to operate on propane. This is used for the control circuitry that calls for cooling as required.
The fridge won't light while the battery is disconnected, but should start right back up when the battery is reconnected (the pilot on ours was a manual light, and would stay on without power).
HOWEVER, you probably don't need to disconnect the battery to charge the battery though. I would expect your unit to have a 12V converter and charging circuitry that charges the battery when AC is present. So your battery is charging while your generator is running and supplying 110V to the TT, or while you are on Shore Power.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2012 Chev Traverse LT with TP