Yes, it certainly is a possibility: his memory for arbitrary information is good, arguably he doesn't understand emotions (that is what Watson thinks).

In the BBC Sherlock series he definitely is portrayed like that, but in the most recent (as far as I know) he is clearly BP (also played by an actor with BP, whose name has now escaped me).

Of course since he is a fictional character (based on different persons in real life Arthur Conan Doyle knew) he could (and probably is likely to have at least one) co-morbidities you can think of.

I was diagnosed both with ASD and SZA/BP. We now figured out (a few different clinicians) that ASD is highly unlikely, it being difficult to distinguish from disorganised SZ, so it could be that he really only has a psychotic disorder.

He needed lots of nicotine to be able to think. That is a major clue. He also didn't sleep or very little when "manic"/manic. He needed total independence and has no routine to speak of.

Those are all reasons why ASD is less likely. A highly rational mind is not enough: psychosis is highly rational and facts to reason with can protect you from becoming irrational, losing control. So many with SZ also like facts. The only difference with ASD is that they are very practical: that certainly goes for Holmes.

ASD is (regarded as being) highly overdiagnosed and psychotic disorders are underdiagnosed. ASD incidence has really been very unstable: has risen tenfold in not that many years. I tentatively assume that is because it is a diagnosis without pharmacotreatment, so more "safe" to diagnose, for the psychiatrist mainly.