So your airline is clear,any failure after the FAF would mean a go around unless in viusal conditions.
Failure such as? Du failure?
No, it was probably poorly worded on my part. Total loss of AP/FD would be a reason for a go-around as RNP approaches have to be flown in LNAV/VNAV and that only available with either FD or AP working and engaged. As of course would be the usual ND/scratchpad messages (UNABLE RNP/VNP etc). DU failures are not mentioned and as the required information is still available they are not a reason for a go around. NNCs have to be completed by 1000ft, same as any other checklists.
LOC approaches are flown in IAN and therefore approach mode (which uses LOC and GP). However VORLOC/VNAV is a valid backup mode and VORLOC/VS is a secondary backup mode. So yes, if you are done with every required procedure by 1000ft, sure you can continue. Although it might be a better idea to go around and set up for second approach using the basic modes.