As far as I can tell, some nasals don't seem to require nasal aspiration. For example, [m] and [n] seem to just involve oral occlusive voicing. I can plug my nose and still make such sounds. It surely sounds odd with a plugged nose, but the consonants are still distinguishable to me. If nasal passages aren't required, then is it really right to refer to them as "nasal consonants"? Or, am I missing something and the nasal passages are still required to seem degree?
Plugged nasals still involve the nasopharynx, even if air does not flow through the nares. The term "nasal" refers to a class of normal speech sounds where air does indeed flow through the nostrils, and doesn't refer to sounds produced by putting a cork in your nose. Our terminology is based on facts of normal speech. Languages simply don't use plugged-nose "dasals", so we don't have a term to refer to them. A dasal® is acoustically distinct from both an oral stop and a nasal. Nasals and dasals have a nasal side-cavity (and corresponding antiresonance), but the side cavity for a nasal is a tube open at both ends whereas the side cavity for a dasal is a tube close at one end, which changes its resonance frequency. You can probably identify the dasal based on the distinctive resonant pattern on surrounding dasalized vowels in plugged "ama".
This recording contains [aba], and [aMa] where "M" is dasal [m]. In [aMa], the consonant is across-spliced from a dasal utterance of ama – the point is that the similarity between nasal [m] and dasal [M] comes from the vowel context, not the consonant itself. By cross-splicing a nasal versus dasal consonant into an oral vowel context, you control the perceptual effect of the effect on vowels. If the utterances sound the same, that supports the view that the acoustic properties of the consonant are themselves fairly irrelevant (what matters in their effect on other sounds). If the utterances sound different, that would indicate a perceptual role for the subtle acoustic differences in the consonants.
If the acoustics of the consonant itself is not the main source of the perceptual distinction between oral and nasal consonants, you also predict that cross-splicing [m] into an oral versus versus nasal context ([aba] versus [ama]) would still maintain the difference between b and m. That is the "different sound same context" condition. In this recording, we have ordinary [m] spliced into the vowel context of "aba" and "ama": that is the "same sound different context" condition. If the two utterances sound the same, that would support the view that the acoustics of the consonant itself plays an important role in perception, and if they sound different that supports the view that the consonant acoustics is relatively unimportant.