Both your ON-BOARD CONVERTER and the BATTERY provides 12VDC POWER to the 12VDC POWER DISTRIBUTION CENTER.
You should be OK operating your setup on shore power without the 12VDC BATTERY connected. The older units did have some models that needed the battery to better regulate the on-board converter but since your Cougar is 2012 model it should be equiped with a better converter/charger unit.
You might grab the model number of the on-board Converter/Charger and let us know just to be sure.
I personally would keep the 12VDC Battery connected in the system operations but that is just me...
You should be aware you will not be able to pull your trailer without a on-board 12VDC battery connected as this provides the necessary 12VDC power to operate your trailer brakes in case the trailer becomes disconnected from your truck when being pulled. This is a DOT requiement to have if you are using electric brakes on your trailer.
If your run-away trailer causes damage to other property or worse your trailer insurance may not work in your favor if it is found that you do not a battery installed as required by DOT.
Just my thoughts
Roy Ken
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS