No AC to DC converters are common, DC to AC are not, they are optional, plus most campers if you tried to run your A/C off batteries they might last 10 minutes if your are lucky, Likely less.
The fridge however is another matter, Is it a "Residential" type compressor fridge.. A modern high effiency Danfoss Compressor Fridge (highly unlikely) or an RV type Absorption cooling unit
Fridges too draw quite a bit of power 100-1000 watts depending on the make and model) if run off AC.
A common group 24 battery, at teh 20 hour rate, has about 400 watt hours of usable power. Think about this,, At the rates we are talking about that goes down, way way way down.
(Except for the Danfoss unit, that one can run 10 hours on a PAIR of Group 24, about 3 hours on one).