You didn't list the year of your 37F. I looked through the 2011 manual for a 37F and it only mentioned a 1000 W inverter, and no mention of a separate battery disconnect switch. Without reading through all the other years' manuals, I'll make a guess and you can read the appropriate manual and see if I'm right.
Winnebago Industries
An inverter is not usually left on all the time because it can quickly deplete the batteries. It is used for a quick use of microwave or some other 120v appliance. It can be left on while driving, since the engine alternator will keep batteries charged, or when on shore power because the charger will keep batteries up.
Your switch might simply be a power switch to turn the inverter off.