Thank you for an interesting question, I had never thought of it.
The self enrolment plugin doesn't appear to have anything similar in the settings (see your moodle for this url - substitute /yourmoodle.example.com with a proper domain name - http://yourmoodle.example.com/admin/settings.php?section=enrolsettingsself).
Enrolment methods work with plugins, so for each way of enrolling in a course there is an enrolment plugin. So if you want to enrol users to courses in a certain way you either configure one of the enrol plugins (the link is in the site settings block) or find another plugin online to download and install, or write your own plugin.
I searched online and came up with a discussion here https://moodle.org/mod/forum/discuss.php?d=209799 but I have never heared of that plugin plus it's not for your version of Moodle.
More info on self enrolment: http://docs.moodle.org/23/en/Self_enrolment
(that's the link for the new version of Moodle though)
I hope I am missing something and that the procedure you describe is possible.
For how Moodle works, you have the tracker site that you can use to request features and bug fixes, and participate in the creation of Moodle.
I wanted to write to the plugin coder but his Moodle messaging has limitations.