Ear training is absolutely worth it! Whether you study intervals/chords yourself or in class, w/CD or DVD, it will improve your ear. However, I don't think that would necessarily lead to absolute pitch.
I'll tell you how I learned (or found out) - as a freshman in High School Band. We had one of those tuning machines with the turning dials (this was way back in the 60's, LOL). I learned how to come in, sing a note, and stop the dials on Bb - didn't take that long, and that is when I realized that our piano at home was about a half-step flat...
BTW, I have read about studies that claim that more people in countries with tonal language (like China, Vietnam) have perfect pitch...