An Airbus does not normally fly a VOR approach procedure. It flies a FMS guided overlay approach. The aircraft wouldn't know or care that the VOR is working or not. This is obviously provided you have GPS Primary. The legality to fly a NDB or VOR without the station working lies with the regulator. (see FAA C300 approval). I'm not sure if OpsSpec C300 have been cancelled or superseded.
OpSpec C300 gives authorization to conduct 14 CFR part 97 non-directional
radio beacon (NDB), NDB/distance measuring equipment (DME), very high frequency (VHF)
omni-directional range (VOR), and VOR/DME instrument approaches using Area Navigation
(RNAV) as a substitute means of navigation.