Yes. In the database, the id of the member who added the tag is recorded (in the bb_tagged table), so if you had an offensive tag, you could find out which member added it. I don’t know if there’s a plugin to make viewing and managing the information easier than using something like phpMyAdmin.
Also, admins can edit everyone’s tags, but a user can only add tags, or remove tags they added. They can’t remove or edit other people’s tags. It looks different when you’re logged in as an admin.