I think that what you are looking for would be to be able to claim a review item for when a user needs approval. Flagged posts in the review queue can be claimed by a staff member. When that is done, only the staff member who claimed the flag can act on it. A similar functionality is not available for pending users in the review queue.
You could allow users to signup for your site without approval, but protect some or all of the content on your site so that it can only be accessed by members of a group. You would add users to this group when they give your their call sign. For details about setting up categories in this way, have a look at How to use category security settings to control access to content.