John,
Welcome to the Gulf Stream Owners RV Forum!!
I do not leave our coach plugged in 24/7 only because we keep it in our community storage lot and their is not an outlet available. Many do leave theirs plugged in, but check your battery fluid level frequently so they do not go dry.
Only you can answer if you have an inverter/charger or converter that chargers your battery bank.
Gulf Stream usually installs the Xantrex Inverter/Charger in the compartment that the power cord stores in.
Here is a picture of what it looks like:
If you don't have one of these, then you have a converter.
Ron