The external database is "passive" and does not send the users over to Moodle, but answer on request. If you want to encourage users to log in for the first time you may do something like this: In one of the courses (with free enrollment) you can write a note with information about where they find the Friday cake. This information is hidden in a certificate and tell them that only employee with the printed certificate will get the cake. Then you copy the url from this course and send a mail to everybody to tempt them to click on the link. You will of course tell them that they can use their well known usernames and passwords.
I am sure you will figure out a much better idea, but the point is that we need to tempt them to log in for the first time.