BuddyPress.org

Well, if I understand correctly it certainly seems possible, considering its pretty much the way that WordPress installation goes.

You install WordPress and are provided a login (“admin”) and a randomized password.

If you’re looking for code to try to tap into, or an example of how to go about it, that would be where I would look first?

The next step in your theory would be to consider how to handle spam registrations in the event that user never sees the pw and never logs in to your website. Maybe take a look at the Register Plus plugin for WordPress.org to get some ideas also?