The following information is regarding TuneCore's Publishing Administration service
Yes! If your song is not distributed through TuneCore (or it's being sold on multiple releases, such as through a label or as a cover song by another artist), after you have signed up and paid for TuneCore Publishing, simply click the "Manage Compositions" link on your Composition Manager where it asks "+ Add Compositions” and complete and submit the form that appears.
It is imperative that you include key data points such as the Performing Artist, Album Name, ISRC Number and Release Date in your song submission. Including this data maximizes the chances of making a match at the various societies which ultimately means more royalties. For more information on the importance of data in song registrations, please read this blog post.
Note that if you are submitting songs that are distributed through TuneCore, these key data points are automatically included in your song registrations.