Does it matter who is the registered agent when sending in copyright info?

Why is the producer sending the copyright applications through his company, why is anybody sending split sheets to the Copyright Office, and why are you asking about who the registered agent is? Normally a musical composition's copyright is owned by the songwriter(s)' publisher(s)/owner(s), and then the publisher(s) pays the songwriter(s) 50% of the total income. The Copyrght Office doesn't care or want to know what the splits are on a song, but it's good, if the information is correct, that that's being put in writing to avoid later disputes. See my songwriters' Legal Guides linked below.

Does your artist have a publishing deal, or are they self-published? If you haven't created a publishing company for them yet, why haven't you? Sometimes producers do co-write songs of certain genres (notably, hip-hop), otherwise they're usually paid, if at all, by a percentage of artist's points from a record deal. They are never, unless the producer also has an active music publishing business, publishers. There's no reason for your producer to appoint himself agent for these copyright registrations- these songs are potentially very valuable to your artist and you should not be relinquishing any control over them to this producer. If your producer has appointed his company publisher and himself 50% co-writer, he's appointing himself recipient of 75% of the songs' income. If you're this artist's manager, you should make sure your artist's work is not gettting misappropriated by this producer.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

The copyright office does not deal with financial arrangements .
The only one that matters is the author. The second important person is the owner, if any.

DISCLAIMER: This answer does not constitute legal advice, and should not be relied on. Each question is fact specific and requires a comprehensive evaluation and consideration of all the facts and documents at issue. This answer does not create an attorney-client relationship.