There is no regulation (for private flight) prohibiting this practice and it is far safer than say flying an NDB approach using the ADF. Airlines do this already - they often fly NP approaches using the FMS navigation but they check the ADF at the top of descent for example, and this is a CAA approved procedure. You are flying the published track but using the GPS for guidance.
A small correction IO, when flying an NDB approach, we don't check the ADF at the "top of descent", we monitor it throughout the approach as per a standard NDB approach. The autopilot is connected to the LNAV track, which is derived from the FMC database and the aircraft position is determined by GPS input (much the same as a 430/530 set up). The primary means of navigation is still the ADF and tracking must be monitored throughout the whole approach (as well as monitoring the ident). Normal errors are allowed for the flying of the approach, but as expected the GPS nails the approach with the needles never deviating more than a couple of degrees, therefore within limits for that approach. Technically you're flying the NDB approach but the autopilot is flying a copy of the published approach track with the position fixed by GPS. The CAA don't need to approve it as we're flying a monitored NDB the whole time.
What the CAA have recently approved are RNAV approaches (eg LHR 27L) which do not require monitoring of any ground based aid to complete the approach.
In my SPA IR, I was encouraged to fly the GPS based approaches and monitoring the ADF needles ensuring they stay within limits (which of course they do). The ADF remains therefore the primary means of navigation.