DT Register does store registration records in database tables, but the only way for user info (name, email, address, etc) to be remembered is if the user logs into the site. Otherwise DT Register would have no way of knowing who was trying to register. The default joomla user system does not store any data outside of name and email. That is why CB is very useful. When CB is installed, DT Register will create additional fields for address, city, phone, etc. When the users have this data filled into their profiles, it will be auto-populated into the event registration forms if the user is logged in. It is a nice feature to utilize.
CB 1.2 is much improved over the 1.0 days. I hated it back then myself, but it works very well now. There are a couple other options out there, but not that are integrated with DT Register yet.
DT Register does not add public users to the Joomla user database, with or without Community Builder. We will be adding a new plugin for that very soon.
For now, it is a one-way situation. If you want to make sure all users have an account on your site, then yes, make your events in DT Register "private" so they'll be forced to create an account first.
In the new 2.6 version, JomSocial integration with a couple of plugins will also be an option in addition to the remaining option of Community Builder.