With two medium sized OEM marine hybrid batteries, you should be able to run the fridge for a day and still be above the happy spot of 50% State of Charge. That assumes fairly modern fridge, typical inverter efficiency, and typical parasitic loads, also. It would definitely be something I'd measure to be sure.
Typical 120V refrigerators use 80-120 watts when operating. The duty cycle is typically 1:4 or 1:3 (depends on ambient and door openings). One fairly accurate way to estimate power consumed is to divide the KWH usage label that is referenced for a year's consumption (yellow Energy Star label on the front of every fridge in the USA) by 365. That will be average daily power consumption.
FWIW, I run a small 120V dorm fridge (80 W'er) off 300AH of battery capacity, through a 1000W inverter. The 12V system is charged by a single 235W solar panel. If the Sun shines, it will run continuously.
I'd bet that if you parked the coach for a few hours and the interior was airconditioned before you parked, the temperature inside the fridge would not rise but a few degrees, even if not powered.