The four GC batteries should be enough while in transit or a short over night as long as the batteries are in good condition and hold a charge. Long term off the grid without either solar, running the generator or even the engine to recharge might be a problem. A residential fridge is very power efficient because of the consumer driven demand for appliances that use as little power as possible which helps. Plus the fridge should stay cold for several hours without power as long as you limit opening the doors. Also, if your coach supports, you might have DC from the engine alternator feeding the house batteries which the inverter can use when the fridge compressor is running while going down the road.
Inverter needs are going to depend on which fridge you choose to replace the Norcold with. Owners have report good performance with a certain Samsung model but I can't recall which one it was. I would budget for it just in case. Certainly won't hurt going pure sine wave.
