As a caveat, I don't have perfect pitch, but with a good bit of training I've developed a decent sense of relative pitch as well as other ear training related tidbits like hearing chord qualities or picking out a chord progression by ear. (And as a footnote, having decent relative pitch doesn't mean I can sing worth anything, it just means my ear is more capable than before of discerning the melodic and harmonic movement of a song.)
In practice, it hasn't been of much use to me in playing drums. It does, however, free you from the "stupid drummer" stereotype when the band you're playing with actually realizes you fully understand what they're talking about, or when you make an intelligent suggestion outside of the realm of drums. I wouldn't train your ear to make yourself a better drummer, but it does make you more of a professional. My two cents, anyway.