As far as I know both my T and pdoc only have Facebook and LinkedIn. Their Facebook is private. I've never send either of them a friend request. I don't think they would accept. They never said anything about it, but I think most therapist or psychiatrist wouldn't be Facebook friends with their clients.
I would want to be Facebookfriends with them, but I don't think it would be good for me, at least not while I'm stil in therapy with them.
And I don't want to risk a rejection, so I would probably never try to send them a request.