I think that chances of a cop asking if you live in your RV are pretty slim. As far as a search I think that they would need a warrant unless you give them permission.
We've been fulltiming for over twenty years. We often spend the night in Walmart,other big box stores and casinos. We boondock on public land. Occasionally we spend the night on the street when we're visiting people. We've never been questioned. If your RV is ratty, if you park in the same spots for weeks or if somebody complains you may get questioned. I know that the national forest in Arizona around Flagstaff has started cracking down on people who overstay their 14 day boondocking limit but that's the only instance of a problem that I've heard about.