homerj, the answer to your Q (in Europe) is ...
If the route (SID) is designated 'P-RNAV' then the availability or otherwise of any VOR is irrelevant. VOR is not a valid P-RNAV sensor. Your RNAV system may use VOR information (as well as GNSS and DME, and INS perhaps) but it is not a REQUIRED sensor for P-RNAV navigation.
Routes that do include VOR/DME radial/distance info are probably designed to B-RNAV standards - this is allowed in any event above MSA, and below MSA is allowed where terrain/obstacle considerations permit use of B-RNAV criteria. So if the chart does not specify 'P-RNAV' or RNP-1, then B-RNAV compliant equipment may be used unless your equipment relies on that inop VOR.