Just pulled my rig south which was about 1600 miles and took a week doing it. Spent a few nights in different campgrounds, one night in a hotel, Bass Pro Shop, and a Cracker Barrel. Never once did I unhook, plus I had a fridge full of food and running on gas.
I would think you have a greater chance of wrecking something if you keep hooking and unhooking. Every time you do that you run the risk of forgetting something.
If you're worried about the fridge being out of level then all I got to say is I would be more nervous about the rig rolling away because you found one extremely crappy parking lot to stay in, and a much better one is just a few miles down the road. Fridges came a long way since the 70's when it comes to lifespan.
I unplug the truck, I have a Chev and it's suppose to be able to be drawn down if left plugged in.