How can I convert anonymous commenters into registered users?

The register_new_user triggers after the user has been created when the register_new_user() function runs and it will give you the $id of the new user that has been created.

If you are using register_new_user() you dont need a password field, wordpress will create one a send it using the email provided to the user.

So yes, using the function will create the user and generate a password, and this logins details will be send to the user.