Right, I checked the FAQ at SoundExchange, and what they cover is the royalties for the (p) which is the sound recording, not the (c) which is the copyright.

So, in case you as a songwriter own the (p) the soundrecording, as well as the (c) the copyright, you can use SoundExchange (and others) to collect for you. This sometimes does happen, if you have recorded and released a song you have written yourself, or if you as a songwriter have paid for a work-for-hire, and thereby also own the soundrecording (p).

The songwriter who has no share in the soundrecording, the (p), are covered either by the PROs or in the case of indie artists who self-publish on iTunes, CD Baby, Bandcamp and others, these companies are obliged to pay out royalties directly to their clients.

From the FAQ "SoundExchange collects and distributes royalties for the featured artist and the sound recording copyright owner when content is played on a non-interactive digital source."

See more at: http://www.soundexchange.com/generalfaq/