This word may be uncommon enough that its connotations end up being ultimately about individual opinion. None of the dictionaries I have just checked give any mention or relevant samples to indicate any inherent connotation in the word.
That said, to me, ‘abstruse’ has a definite negative connotation, like ‘obscure’ and ‘arcane’.
Most words that mean ‘difficult to understand’ tend to have a negative connotation, simply because making oneself clear and easy to understand is generally considered a virtue (unless you’re a philosopher, in which case I imagine the connotations are probably switched), while failing to do so is considered something undesirable.
The only words I can think of in this semantic category that generally have a positive connotation are recondite and (especially) esoteric. Both these words refer to something that is difficult to understand not because it is unclear and muddy, but because it is intricate, specialised, and rarely seen—and exactly because of those qualities, it is seen as being somewhat precious.
It has the negative connotation that one is about to undergo surgery!
Since no surgery is completely without risk, and most is followed by a period of pain or discomfort, any expression describing it inherently contains a negative.
For that reason, we might euphemistically talk of "going into theatre"; a form of synecdoche, where the act of going into the place where surgery is performed stands for the whole process of going in there and having surgery performed. (We also use the same euphemism of the surgeons, theatre nurses, anesthesiologist, etc. who perform the surgery).
"Go under the knife" is a mild dysphemism, that doesn't add a negative connotation so much as focus on that which is already there.
This sort of bluntness can have a sort of euphemistic effect though, in a manner not unakin to gallows humour. Some people find it more comfortable to address the negative than to talk around it.
This sort of bluntness would require a degree of familiarity to be appropriate, and from that the ability to judge whether the person hearing it would indeed be the sort to prefer it.
It's also favoured as a dysphemism in more impersonal, informal writing. In journalism we'll find it used more of elective procedures, than for emergency or clearly required procedures, because "chose to go under the knife" both efficiently covers that a risk, and often a subsequent period of pain and discomfort, was entailed in that choice, as well as being a more vivid expression than the alternatives.
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I imagine that your US colleague was referring to the expression, "out", used when a LGBT (lesbian, gay, bi-sexual, trans-sexual) person goes public with their alternate-lifestyle orientation. It's referred to as "coming out of the closet", and has been morphed into "outing" or "outed" when it's done to someone by someone else: