No, we don't currently support using the CB registration flow for new users. You can use our automatic registration flow to have them automatically registered, the Joomla registration flow or JFBConnect's registration page which can show fields from CB to be filled out by the user.
We do support going through the registration flow of JomSocial and EasySocial. We would like to add a similar option for CB at some point in the future, but CB's code is extremely difficult to integrate with. I'm not sure we'd ever be able to do what you're looking for and, until then, the only options we have are the ones mentioned above.
I hope that helps explain,
Alex