The add connection link is just an HTML link, but adding it self where you of course will not get the JS pop-up to send the usage a message with the connection request or anything of the sorts. Please search as link has been provided numerous times.
However, the issue comes with protecting an entire profile. There's nothing as far as I am aware that can do this. You can use CB Privacy, but this is user by user privacy controls as in User A could require someone to be a connection to see Tab B, but maybe only require them to be registered to see Tab A. Of course this would be entirely different based off how User B configures their privacy.