Your fridge does not depend on your caravan battery but your car battery (should be wired in such a way so as to only draw power when the engine is running).
as above but each of the battery terminals need to be wrapped in a plastic bag and tied up to prevent shorting or fire,simply because the car is still tying to charge a battery that is not there.mainly the red one.
------------- the only silly question is the one you do not ask.
JTQU has confirmed my thoughts that the newer fridge wiring system does detect the battery being online or 'out of the loop', which makes me think that running throught the 12S the fridge will not 'read' that there is a connection and seek power, and the fridge charging relay may not function as it too detects that there's no load to supply.
I know that the old system would run batteryless if the + and - battery terminals were linked with a wire.
------------- There's nae pooches in a shroud, so spend it before the Government does it for you!