Galleypower, you don't say whether you are a commercial or private operator, or where you are based (UK/Europe, US or elsewhere).
If you are employed in UK/Europe then your airline will probably be working to JAR-OPS or EU-OPS regs, in which case -
- If it says GPS (or GNSS, same thing but more correct) on the chart then you must be receiving valid GPS/GNSS data.
- If you are flying an overlay procedure and lose the GNSS, you may revert to the conventional 'reference aid' and continue, if you lose the reference aid (VOR or NDB) you must execute a missed approach.
- If it names a VOR or NDB aid then it is an overlay procedure and the RNAV system may only be used if the underlying 'reference aid' is available and agrees with the RNAV.
- An RNAV (GNSS) Approach is what ICAO (Doc 9613, the PBN Manual) calls a 'RNP APCH', and requires multi-sensor (ie, GNSS and DME at least) RNAV kit with a specific standard of 'on-board monitoring and alerting' (their phrase).
- For a GNSS (Only) Approach you need two independent GNSS receivers for starters, and, I believe, space-based augmentation system (SBAS).
Your '(GPS) VOR RwXX' I've not seen before. The principle in Europe at least is 'If it says GPS you must have GPS', if it says VOR (or NDB) you must have VOR (NDB).
We're talking about RNAV or FMS based approaches here, and an approach designed for VOR or NDB but coded for the FMS (ie, an overlay) may only be flown using the FMS if the underlying reference aid is available and confirming the FMS accuracy.