Find the owners manual for your converter and read it to be sure of the functions available. Search the internet, if you have the converter manufacturer and model number, you can usually find the manual if you cant find the one that came with your MH. From your initial post I'm assuming your converter has an equalize function built in and you will be using it to equalize your batteries. (not a remote smart charger) You didn't state what type of converter, refrigerator, or batteries you have. Late model Tiffins should be close to top of the line.
Typically if you have a 3 way fridge, its logic center first chooses 120 volt power, if available. If not, usually you can choose to run it on 12 volt or propane should you wish to. The AC runs on 120 volts from shore power/generator and should not be affected by any battery charging function, however depending on how the coach is wired, the coach 12 volt consumers may be. Leaving all other coach 12 volt loads shut off during equalizing should prevent damage due to higher than normal equalization voltages. (+-15.6 volts for +-2 hours on typical flooded lead acid deep cycle batteries)
If you have a 2 way fridge, 120 volt/propane the fridge does use 12 volts to power the logic board (the 3 way does too) in which case you can just shut the fridge off for +-2 hours and turn it back on when you are done equalizing. Shouldn't hurt a thing.
Chum lee