I fly B777s and we regularly fly NPAs in LNAV and VNAV, but ONLY when the approaches can be line selected from the data base. This ensures that details of the approach cannot be entered mistakenly due to transcription errors.
I would suggest that, if your avionics suite does not include an approved data base or it's military equivalent for the approach being flown, NPAs should be flown in one of the more basic modes (VORLOC or HDGSEL).
That notwithstanding, I don't see a problem with flying in MAP mode on the ND, as long a source of raw data is available to check correct tracking. Most EFIS systems have the capability of putting VOR, NDB or ILS data on either the ND or PFD even in Map mode. Provided your procedures ensure raw data is available in some form, MAP mode gives a better situational awareness than a full-compass rose type VOR display.
The question as to whether your avionics has sufficient sensor capability to fly certain approaches is covered by RNP/ANP. Do you have an approval as to the Actual Nav Performance of your gear? Generally to fly an NPA without tracking guidance, you require an RNP of .3NM.
Hope that helps.