@ Eric
In short, if I read this correctly, no this is not possible since Connections does not create user accounts.
What I recommend is user a user registration plugin that upon a successful registration redirects to their “Edit My Directory Entry” admin profile page. I know many users have such a setup, but I do not know what plugin they used to handle user registration … there are many freely available one out there.
For what you’re trying to accomplish, you would not need to use Form. Currently the primary purpose of Form is to take submissions to be listed in the directory from site visitors, not intended for site users, that is what Link is for. Hope that make sense. Now with that said, they next version of Form, when Link in installed and active, will allow a user to maintain their entry from the front end. I’m still not quite sure how I’m going to reconcile user maintaining their entry and allowing visitors submit listings but I’m certain as I play with this new feature I figure a way to make it work.
Hope that helps!