That would be unprofessional and since Sweets is so young he is constantly defending himself. He is constantly having to proove himself to the team and remind them that he is a doctor (like during Booth's interrogation) He is trying to command the team's respect so I doubt that he would ever make himself vulnerable. They may not respect his profession but they are starting to befriend the man. Sweets is fun.
I'd like to see him on his own therapist's couch giving his view of each one of them - deconstructing them, now that would be interesting.