There seems to be a lot of confusion about the inverter for the Cedar Creek. The inverter is only connected to the residential refrigerator, period. No other a/c outlets are supplied by the inverter.
The inverter can be left on when connected to shore power. It is drawing minimum current from your battery and your battery will still charge. It will not pop any a/c breakers. It is just in standby mode waiting to sense when the shore power a/c to the fridge goes away. It will switch over in milliseconds if the shore power should go away, say at 2AM when you are sleeping or when you are away from your rig and there is a campground power failure. (not that that ever happens
I generally turn mine on when I pick up the 5ver and then after hooking up to shore power I turn it off with the button on front of the unit. I've also left it on while connected to shore power. It is doing nothing at this point, just in standby. There are status indicators on the front of mine that tell me when 120vac is being used and when it is on battery power supplying the a/c to the fridge.
Just remember if you do turn it off when on shore power to turn it on before you depart your campsite.