The battery powers basically everything electric in the trailer except for:
- Air conditioner
- Microwave
- All the 120v (household style) outlets)
- The converter/charger which charges the battery
All of those items above are powered by plugging your shore power cord into an outlet. Everything else is powered by the battery.
Even if you turn off everything in the trailer there are parasitic loads, things like the propane alarm and memory settings on entertainment system that are always on and draining power from the battery. These parasitic loads can drain a fully charged battery in 1-2 weeks.
If you are able to plug into a 120v outlet at home the converter/charger in your trailer will charge the battery back up.
Having the battery drain below half it's capacity is damaging to the battery. If you cannot plug in to a power source you should use the disconnect switch.
Except if you are using the refrigerator it needs to use the battery or be plugged in, even when it is running on propane.
So basically if you are parked in your driveway you might as well plug it in and keep the battery charged. But you should also check the water level in the battery at least once a month until you get an idea how fast the water is evaporating. Letting the water level drop and exposing the plates is also damaging to the battery.