Snopes chimes in on the status of "poor man's copyright," the practice of mailing materials to oneself to assert a date of creation in case you ever find yourself in dispute over ownership of a song or any other creative work.
Anecdotally, we have all run into someone that has used this technique in the past. But, with postmarks so easily faked and such a high perceived fear of song-swiping, registering your work with the Library of Congress is a great insurance policy on your future earnings.
With copyright registration at only $30, you are far better off paying the fee and getting your works in the system. Remember that you can send off an entire collection of works under a single filing, so if you're stuck for cash, that option is at least better than nothing. Yes, you do own your copyright the moment you create the work, but the more external validation you receive, the better, especially in the eyes of the court.