Well if you don't talk to him then nothing is going to change. So if you think this is an issue then, for sure, talk to him, what do you have to lose? It sounds like the relationship is approaching make-or-break anyway.
It could be he knows (maybe he just hasn't told you), or it might be something that he wants to investigate further and see his GP about, or of course he might not have Aspergers, he could just be odd 
However you have to bear in mind that diagnosis isn't a cure. If he is seen by a psych and formally diagnosed he is still going to be the same person with the same issues and behaviours. It might make him happier within himself and perhaps more open to try and alter some of things he does, but who knows.