To help anyone who may still have questions regarding this topic, I received this information from a fellow FP'er (shoutout to Pow Bob)
"They passed a law back in the day, (The Audio Home Recording Act), when digital music came on the scene in the form of CD's and MP3's. The music industry was going to sue companies like Sony, because they were manufacturing items that consumers could use to reproduce the same high quality music for free at home, causing the music industry to collapse. Instead, the law provides that these manufacturing companies all have to pay royalties to ASCAP or whoever, so that some of this money could be recovered.
So, it would certainly seem to be a no-brainer. Of course you want ASCAP to represent you for these royalties, just like the reason we're joining in the first place, to collect royalties. I just don't understand now, why one would choose No for that option. So, I just called ASCAP. I asked them who would answer NO on that option, and she said only people who don't understand it, or people who have another agency/entity that is doing it already. So, for a rookie beginner, by all means, answer YES to this option, or there is a period during the year I believe when you can sign up for it, if you elected not to and got ASCAP membership. You can post this stuff to your thread from years ago if you want, I think it's pretty accurate."
Hope this helps someone else out.