Ok, how about this?
Do you agree that an overlay approach is an RNAV approach? If yes, then:
Do you agree that if a VOR is unavailable but there is an overlay you can still fly the approach using the overlay (RNAV)? If so, then:
Do you agree that if the VOR is unavailable and there is no overlay, you may not fly the approach, since there is no RNAV procedure?
If you understand all that, and understand that an RNAV has as much relationship to a VOR approach as an ILS does, what is this discussion about? You can do RNAV, or ILS, or VOR, or NDB. You can't do a combination of them.
ILS requires a functioning ILS transmitter
VOR requires a functioning VOR transmitter
NDB requires a functioning NDB transmitter
and RNAV requires a specific navigation performance be met along with crew qualification etc.