The repository pattern in the original example would allow you serailise your objects to whatever datastore you want. His object design isn't that great for being persistence ignorant though. I would instead do something like this.
Course - Aggregate Root
Student - Aggregate Root
RegisteredCourse[] - RegisteredCourses - An array objects with date time of registration, and id reference to course.
The method for adding a course would simply create a new RegisteredCourse and place it in the registered courses array.
_studentRepository.save(student) would be a simple matter converting this in memory representation into sql.
I'm not big fan of using lazy loading, and direct references to other aggregates inside of other aggregates. This makes mapping these models without ORM difficult.