Will 32-061 Drawer slides lock in place for RV

The 32-061 drawer slide kit is "self closing," which means that the track is slanted in such a way that the drawer will not drift open on its own. That said, these aren't strictly speaking locked. They will open with enough gumption, so I can't say for sure if these are going to pop open on a long trip if you install them in your RV drawers. It would depend on what kind of gumption you expect! None of us here personally own an RV so it's hard for us to predict.

You may want to consider a back up locking method just to be safe, something specifically made for RVs or at least something you can fashion that will serve the same purpose. A local hardware store may have some ideas for you, especially if they deal in hardware for RVs.