Will adding a student to my Canvas site grant them enrollment permission?

No. Canvas is the learning management system and it has no impact on formal instructor permission or course enrollment. 

If instructor permission is required in order to enroll in your course, students must submit the permission request through their Yale Course Search registration worksheet. If you grant permission to the student, they will then be able to enroll and gain automatic access to your Canvas course site.

Instructions regarding reviewing and granting permissions requests are here.