My first thought about the pale ichigo was that...since the bleach universe seems to revolve around reincarnations back and forth between soul society and earth, that maybe the white ichigo is ichigo's SS-alter ego. Like when ichigo dies, he assumes that form, and then when that form dies, he assumes the form he currently is now, once again. Or maybe alternate forms every other death (ichigo has to die now and then again as a spirit for the white ichigo to take over)

idk....that was my initial guess

by this theory, that would mean that the white ichigo is the one that rukia and byakuya were referencing when they said something about him resembling "that guy" just before they left for the SS