You don't HAVE to turn off anything....I do, but you don't have to. If you are using your hookup for keeping the battery charged, one of those breakers will be for the converter's charger and would need to be left on. For long periods of time, I disconnect the battery and put a dedicated smart charger on it and don't rely on the converter. I'm probably paranoid, but I've heard too many stories of converters malfunctioning and overcharging (destroying) a battery to just walk away and leave it for weeks / months like that.
A word of caution just in case you didn't know. Make sure you know both the voltage and amperage of your hookup at home. I've seen a number of people on here plug into a 220V recepticle at the house because it had the same connection as the trailer's 110V.
2012 Chevy Tahoe LTZ - HD tow package
2017 Rockwood 2703WS Emerald Edition