I was looking for a way to grant a classmate the specific admin privileges for uploading yearbook photos alone. It initially appeared that the system would let me do it. After the privileges were assigned, the "upload yearbook photos" link did appear under "Admin functions" for the classmate. However, he gets an error message when he clicks on the link.
Am I correct in assuming that "upload yearbook photos' admin function will not work unless "manage classmates" admin function is also checked?

Yes, that is correct. In order to select classmates for whom to upload photos, the admin has to view the class list, and the class list admin page is only visible to users with the Manage Classmates admin privilege.