Hmmm, maybe you could use workflow-ng for this? The user could put courses in the cart along with other products. Then at checkout create a workflow that takes the user through whatever process they need to go through for registration if the cart contains any products that are in the product class "course".

I built an e-commerce platform (not ubercart) for a client that does class registrations. They have courses for registration and shippable products from the school store. I treated the course itself as a type of product that is simply added to the cart. Upon checkout, if course products are in the cart, the user has to register an account or login. Then it goes through a verification process (is the class full, is the user banned from registration, has the user already taken the course, has the user taken the required prerequisite courses, etc). Then the user has to fill out registration information which gets saved as part of the user record. After payment, the course is added to the user record. Basically, everything is associated with the user record. The user's role is "student".

In Drupal, you could use profile to store extra information in the user record.

Hope that helps.