I am a Bassist and I have perfect pitch in low frequencies. It starts to weaken in mid frequencies, and weakens more still in high frequencies (though I can still "color hear" in these frequency ranges, just not/no where near as well respectively). I can "color hear" notes on my own instrument (Double Bass and Electric Bass) the best, but the ability does pass over to other low pitched instruments too (such as the Tuba, Bass Trombone, lower regions of a a Piano). I can work out chords, but have a tendency to work them out from the bottom up (I will work out the lowest note using perfect pitch, and the rest of the notes using a mixture of perfect pitch and relative pitch). Beyond that level of perfect pitch/absolute pitch/color hearing I have to resort to relative pitch in order to get by.
The timbre of the instrument that someone plays, and it's pitch range (or in the case of a Keyboardist the main range that they play in) drastically affects any color hearing that a person may develop, so no, absolute pitch does not cover the full sound range.
I personally do not like the term perfect pitch as, let's face it, it's definitely not perfect. There are different levels of it too, from basic color awareness to universal color hearing. It is my belief that very well developed relative pitch is probably superior, but getting to that point takes years of practice.