Yes, it is possible!
When a member writes a post, if [Admin only] is set, only the manager of the class can see the post.
The teacher who created the class is automatically set as an administrator.
Therefore, if a member (student/parent) writes an 'Admin only' posting, only the Class manager(teacher) can view the posting.
※ If you want to know who is the manager, please check [Members]. You can also change other members' privileges to admins here.