Does "unbearable" always have a negative connotation?

I came across with this sentence

"As a child he held an unbearable curiosity, he needed to question everything"

Since english is not my first language, I was giving it a second thought and trying to understand if the word "unbearable" was used correctly. By this, what I mean to say is that "unbearable" seems to me as a negative word (unbearable pain, torture, and so on...) . However, the fact that "he needed to question everything" could be an awesome feature of his personality.

From journalism to engineering, curiosity is definitely a good thing, something desirable. I believe that there's some passionate feeling involved in the use of the word to enforce the feeling towards questioning.

I looked for unbearable in the dictionary and of course give me the "not bearble" definition. Going to the "to bear" definition, it leaves the door open for a slightly more possitive meaning.

Does "unbearable" hold any ambivalent meaning or I should assume that every time would mean something negative?

In the former case I should try to get it from the context (or maybe there's a related word that fits better and is used more often to avoid confussion). In the latter case, perhaps the mother of this child had had enough, given the amount of questions, and "unbearable" was correctly used.

It is being used figuratively, a bit of hyperbole, but it is fine to use it in such a way. You could say someone is unbearably good, that their extreme virtue makes being around them insufferable, through no fault of the saint in question.

The term can be used to mean something extremely good as in the novel and film The Unbearable Lightness of Being.

According to this Wikipedia article,

The "unbearable lightness" in the title also refers to the lightness of love and sex, which are themes of the novel. Kundera portrays love as fleeting, haphazard and possibly based upon endless strings of coincidences, despite holding much significance for humans.

The connotation is that the experience is at the edge of pleasure to the point of being just about intolerable, similar to the phrase hurts so good by Mr. Mellencamp