In my opinion, the residential refrigerator will function more economically if powered up constantly, especially if equipped with an icemaker. If you have the coach plugged in to shore power when in storage the only thing that runs all the time is the fridge. The batteries will be trickle charged at all times as well. I have done that with our 2015 Bounder and had very good success. The icemaker stays full and we even leave some juices and other items in the fridge that won't spoil even if the power should fail. In that event the inverter will take over, and I will always check in on the unit periodically during storage, just in case.

We have a residential fridge in our 2015 33d. Inside the fridge there is a temperature control knob that we turn to shut if completely off. The lights will go off when the door is open and then you know it is off. If you do this make sure you wipe it down and then spray with Lysol and keep the doors open so you do not get mold.