My first thought was Shirley Temple. So, no not negative. Just cute and smart.
Well, I couldn’t, but then again I’m not precocious.
Call me weird, but I think the negative part is “little fuck”.
You’ve obviously never met Mike’s son.
“Mike’s son is precocious”. Neutral
"Mike’s son is precocious (paired with a roll-eye) Negative.
I never took it to mean anything other than the dictionary definition, which off the top of my head means something like “sooner than expected.” Little Fred is “precocious” - that is, he’s beyond his years in knowledge, manners, appearance, what have you. Little Suzie entered “precocious puberty” - that is, she got into adolescence at a comparatively early age.