Company SOPs may dictate what you have to do but as a rule if it is not a stand-alone R-NAV (GPS etc) approach then you have to display and monitor the nav-aid. If there is a signifigant difference between the nav-aid and the FMS/FMC track then you must follow the nav-aid (VOR, NDB) or go arround. You must go around if the nav aid shows a more than 5 degree deviation from the published inbound course.
You can fly VOR and NDB approaches in L-Nav and V-Nac (or V/S) but you must monitor raw data and vertical profile. My company does that but flies LOC approaches in LOC/VS