Is it possible for some kind of front end users e.g. authors, to view all the profile data in a list
Sure, create a userlist that's accessibly only by Author users then assign some users to the author group.
including the fields which are marked as "not visible in profile?".
You can try adding them to the userlist as instructed with the previous quote, but you may need to make them visible and instead place them on a tab that is not displayed on profile position then add them to the userlist.
Can this be done by the CB privacy plugin?
No, CB Privacy controls user defined privacy settings for individual fields and/or tabs. It is not dependent on ACL.