An overlay approach shares the plate and minimums with the VOR or NDB procedure, but beyond that it has nothing to do with the VOR or NDB. If you do a GNSS overlay approach you are doing an RNAV approach, which you must be trained, equipped and authorized to do.
The actual VOR or NDB could have been dynamited into oblivion years before and it doesn't matter, because you aren't flying a VOR or NDB approach.