There are three separate issues at play here. First, does the aircraft in question meet AC 20-129 requirements and have approval in the AFM for VNAV. If so then VNAV may be used for the final segment regardless of the type of approach(excluding RNAV approaches).
Second, does the operator have Ops Spec C073 approval per Order 8260.54 to fly VNAV to a DA in lieu of an MDA. According to the Order, an obstacle assessment must be accomplished prior to using DA in lieu of. However, it states the FAA has done an obstacle assessment on all RNAV to LNAV/VNAV minima, all ILS approaches(i.e. G/S OTS), and an approach with a VASI or PAPI. Jeppesen has coded the VASI/PAPI with the ball note "only authorized users may use DA in lieu of MDA". So with Ops Spec C073, an RNAV to LNAV/VNAV minima, ILS G/S OTS or an approach with ball note can be flown to a DA.
Finally, referencing more Advisory Circulars, specifically AC 90-105, would give operator approval for RNAV approaches. Either RNAV(GPS) or possibly RNAV(RNP) with SAAAR approval.
All this enables an operator to use VNAV to fly a constant angle non-precision approach. But as some have pointed out, you can fly a constant angle approach without VNAV path guidance. In fact, even with VNAV approval, there are some ILS G/S OTS approaches where the VNAV path will violate a step down fix. In that case, vertical speed would be used to ensure step down fix compliance, but still flying a CANPA type final segment. Most major airline operators have gone to the DA/DDA minimum only. Regardless of VNAV or V/S on the final segment, once at DA/DDA, a missed approach is executed if runway environment is not in sight.
Boeing has changed terminology as well. They label the approaches either an ILS or an Non-ILS. Non-ILS can included VOR, RNAV, LOC, IAN or GLS for example. 787 and -8 have IAN and GLS capability(I think some 73NG as well).
This has been my experience with Honeywell 757/767-200 200k FMS, 767 PIP FMS, 757/767 Pegasus, 767-400 Pegasus 2000 and the 747-400 and -8 FMS's.