The FAA is gradually updating its procedures to accommodate such a scenario. More and more plates are being renamed as "VOR or GPS RWXX". If that's the case, you don't need to have the VOR.
In any event, even if the approach title didn't have "or GPS", the approach will still be in the database, and you'll get approach sensitivity on the CDI (on Garmin products at least). In an emergency, this is a very useful solution.