Perfect Pitch is a human ability very similar to Relative Pitch. Both are usefull in playing-enjoying music and both have to do with the way someone hears. But, perfect pitch is mistaken sometimes as born-wth ability or othertimes as less usefull.
More or less, I will gently disagree with jossuk. There are no drawbacks in learning Perfect Pitch. There are benefits, that together with relative can develop a very good hearing ability!
These are : 1. to be able to hear what's the different between pitches (why A sound like an A, what Bb sounds like, why that music piece is writen in that tonality, what happens in music when you tune higher or lower) , 2. to be able to identify pitches without a relative one (that means you can tell what a pitch is without starting with a known one, because of no1), 3. to be able to sing pitches without get a known pitch, 4. improves your musical memory (because your mind has another way to remember music). That what I can think for now.
And for the drawbacks, let me explain. If you have both relative and perfect pitch, there is no music confusion. There is no "I can't stand listening to this music because it is tuned lower", because the only thing you hear is pitches, you can not only tell what's reference between them, but also tell what the sound like. In other words, you feel like tuning yourself lower and listen that way.
Of course, it can be tought! To be precise: of course, anyone can recall that ability, because it is something we are born with, but none tell us to practise.
I think I helped!