I cannot see where any LEO would ask you if you are living in your RV, unless you are parking it in a spot that is illegal or in a spot where you are overstaying your welcome, such as a Walmart Parking lot. There are people who appear to be vagrants and are making a nuscience of themselves by loitering or panhandling. LEO's generally will not stop you unless they have recieved a complaint or there are some surrounding suspicious activity.
I personally would never allow anyone to search my rig unless they are in possession of a search warrant.