It is proof that you wrote it when you say you did. You should still copyright the music at the same time you mail the letter. If someone gets your music, copyrights it and then claims to have created it before you did the only proof you have is the letter. In a Civil Court all that is needed is what is called "Preponderance of Evidence". That means one party in the suit only need to present more evidence... 51% to be exact. If you go into court with a "poor mans copyright" and little else nowadays you will get chewed up from the floor up.

