well, basically, as soon as you are inhaling nitrogen under pressure, you are getting narced, it's just that you don't notice the effects until, say, around 100 feet or so, and they continue to increase as you go deeper.
those people who say they've never been narced are wrong. they basically haven't noticed the symptoms. but their performance (as compared to the surface) has degraded due to nitrogen narcosis.
so, essentially, it comes to how degraded your performance gets and how well you can adapt to the symptoms.
so ... yes.. you can dive deep on air. some divers will dive down to 250 feet and over on air.
is it advisable? i wouldn't do it. the Rouses (from the book The Last Dive) died because of impaired mental ability at 280-ish feet due to diving that deep on air).
can it be done? yeah. before trimix, people dove that deep on air 'cause they had no choice.