There is a tracker item for notifications to users of new accounts:
There are also items for teachers to get e-mails notifying them when a student self enrols.
There are forum posts here with code:
However, the problem is that these involve hacks to core code.
1. How hard would it be to have a plugin that sends e-mails to users which have had new manual accounts created. Maybe run once an hour.
2. How hard would it be to have a plugin that sneds an e-mail to teachers of courses when student self enrols in a course.
3. Ditto for e-mail to teachrs when a student FIRST visits a site.
ie no hacks of core.