The easiest way to tell if one of your students is registered is by checking their Role.
Go to the Manage Roster page, found within the professor tools section in your community.
While viewing the course list, check the Role column (the final column in the roster table).
If a student is registered, their role will show as Student. If the student has not registered, they will remain on your roster as pending and their role will show up with the role of "Added".
This means the student was added to the community, but the student has not yet finished the remaining registration steps (like checking out) to become a full member of the community. A student in the "Added" role status would unable to post in the community until they finish registration, at which time, they will appear with the role of "Student".
You can filter your roster by role to quickly see which students have registered and who hasn't.