If someone signs up for the facebook group, then posts "Hi, I'm so and so!" they've gone past the point of non-approval. It doesn't appear that anybody is listing anybody else's name and moniker without approval.
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .