Hi Kijangnim, Denti & Dutchone,
I agree it is permitted to perform RNAV approaches with no ground based radio aids necessary - but they are specific approaches, (called RNAV or GNSS etc).
I thought that if the NPA approach plate specifies a radio aid - then it must be working - else you have to do a different approach.
e.g see Page 37 of this document:
AirbusSafetyLib_-FLT_OPS-GEN-SEQ02.pdf
It shows the same profile as the VOR Canarsie Approach at JFK, except it is called RNAV. If the VOR Carnasie is US - then you can't do the VOR approach - but you may do the RNAV approach - because there is one published.