I think that depends on whether the personal detail in question helps or hinders bonding.

There are many personal things people (strangers mostly) could tell me about themselves that would put me off rather than get me to reciprocate, and probably I've awakened such reactions in other people in the past as well.

Confess something embarrassing or awkward enough, and wave your success goodbye -- just when you thought you were improving social skills by consciously applying social strategies...

Tip: an unflattering but ordinary and relatable experience is best for this. Internet meme images and funny pics are full of those.