The fridge right now is in your main load center and you must have a second one for your inverter.
If they are adjacent to each other and there is enough wire it may swing into the other.
Not sure why you want to do that if the fridge is cold to start with it will stay cold to your next camping area when you plug in again with shore power.
You will need to plug in or run Gen so slides will move out which you should do anyway.
The Norcold only used the 110 for the electric elements when plugged in and not using LP gas.
Here is
a link so you can look up the TSB's on your year coach and you can also get your Brochure and Owners Guide for your coach, just follow directions.
All the links below in my signature have info for your coach.