Next CB Connect will use HybridAuth and the fields available will be only those provided by HybridAuth. You can find these below.
hybridauth.sourceforge.net/userguide/Profile_Data_User_Profile.html
Username, Name, Email, and Avatar are always auto-mapped from the social site when possible.
There will be 2 registration methods. One will register then immediately login with minimal information. This is most simple for the user. The other will pre-fill the standard registration form with their social site information.
All of the above is for next CB Connect release (am currently working on this). Current CB Connect is bugged and not CB 2.0 compatible.