There is definitely a benefit to signing up for CD Baby Pro Publishing, even if you are already affiliated with ASCAP or BMI!
There are two types of royalties that artists can collect for their music: performance royalties and mechanical royalties. Performance royalties are split 50/50 between the songwriter and the publisher. 100% of mechanical royalties are paid to the publisher. Through CD Baby Pro Publishing, CD Baby will collect publishing royalties for artists on their behalf. Songwriter royalties will always be paid directly to the songwriter by ASCAP or BMI.
Since ASCAP and BMI only collect royalties on behalf of songwriters, artists who have signed up directly through ASCAP or BMI are only receiving a portion of all of the royalties owed to them. This chart helps break it down pretty well:
Artists who sign up directly through ASCAP and BMI are only eligible for receive the songwriter (blue) portion of their royalties. Artists who sign up with CD Baby Pro Publishing are eligible to receive the songwriter (blue) and publisher (red) portions of their royalties.