While not exactly what you want to do, Richard Oelmann initially did some work for his theme Handlebar in which it would display teachers and contact details in a special modal window for students.
I also utilized this method for the Fordson theme and when students go to a course they can see the teacher as well as a method to contact them (email/message).
The code in my link might help you gather all the information from the database for the teacher of the course and then you would need to hack the core course overview block or create your own based off that one.
Or you could decide to just include the teacher contact information on the actual course page such as what is done with Handlebar and Fordson themes.
Hope that helps get you started.
Chris