On the Dodge the battery charge line is Hot all the time......so if plugged in the rv can drain truck battery IF you do not have 110V AC power plugged in also
Fridge needs good source of 12V DC to operate whether on AC power or on propane (operates the control circuits)
Fridge needs several hours to cool down properly........so turn it ON now if you haven't already done so.
That is provided the rv is level......fridges don't cool properly if off level and they can be damaged (clogged) if operated off level....even one time. The damage is accumulative.