I discovered that if I set the capability moodle/course:view in the custom role that I created for our users to Allow, it hides them from other participants whilst still allowing them to view the course contents. My custom role users the Student role as an archetype.
Is there any chance that someone can add this to the Moodle 2.3 documentation? Hidden Roles (http://docs.moodle.org/23/en/Assign_roles#Hidden_roles) under Assign Roles only talks about using Other users. It mentions moodle/course:view but not using the method I mentioned above. I came upon this solution quite by chance whilst searching through the Moodle Tracker.