Hard to say. Certainly, whoever's on the bottom of the ticket would influence his decisions, and given Powell's well documented moderate stances on social issues (pro-life, ambivalent-leaning-towards-pro on gay marriage/civil unions), he'd probably pick someone who has more cache with the conservative base.
Not sure where you got that, but Cheney and Powell loathe each other. Powell has all but said that he considers Cheney and Rumsfeld delusional, and Cheney basically bragged about getting Powell fired as SecState. No idea what their relationship was like prior to serving in Bush's cabinet, but by 2004 they probably couldn't be in the same room together.