You cannot legally tow without a battery to supply power to the brakes, if the breakaway cable is pulled.
You can stay plugged in at a campground without a battery, but if the campground power should go out, you will have no water pump and no lights without the battery. Both of those are supplied through the 12V system.
When you are plugged in, the converter supplies power to the 12V system and charges the battery. Without a battery, the converter will still supply the 12V system IF you are plugged in.
My advice? After you get some experience under your belt, don't limit yourself to campgrounds with electricity. Some of the best fun is to be had in more primitive settings.