I think you've answered your own question above. It largely has to do with context. There is certainly no inherent connotation to the word other than self-taught.
There are definitely situations where being self-taught is positive, negative, and neutral.
For instance: A 15 year-old piano prodigy being an autodidact has an extremely positive connotation. (Some would call him a genius . . .)
A neurosurgeon who is an autodidact, well, that might be construed as negative. (Most would call him a criminal.)
I'm a serious amateur photographer who is an autodidact. I'd say it's fairly neutral. (The judgement would be withheld pending the quality of my work.)
Note I strongly prefer self-taught in my own usage.