First of all
to the forum
To answer your question, Yes to both, if all is working correctly. When plugged into shore power your RV has a converter that uses the 120vac and converts it to 12vdc and charges your battery and powers your 12 volt items in the RV, lights, parts of the frig, furnace fan, things like that.
When plugged into your TV your 7way plug should have one of the pins with 12volts on it from the battery. Not all vehicles have this active, usually the factory does not hook up the wire ate the fuse block under the hood or put the fuse and relay in. This is something the owner of the vehicle is responsible to hook up if desired. I attached a picture of the 7 way plug to check for voltage if you have a test light or volt meter. Even once you have voltage to the RV from the TV it does not provide much charge to the RV. It will help, but do not plan to rely on this as a charging method.