That's beside the point. McCain wasn't in on the planning in OTL. In this TL he is, and significantly, Dick Cheney is not. Rumsfeld might not be either for that matter.
Actually, I think you might've mixed up the proposal. Dick Cheney is still Vice President...it's Rumsfeld who is out, replaced by John McCain.
I honestly don't know what McCain would've done differently...heck, maybe it would've been worse...but a few things have to be taken into consideration:
1) There was still a LOT of animosty between McCain and Bush, with 9/11 happening barely a year after the Bush campaign accused McCain of biologically fathering his adopted black daughter. Maybe this is partially butterflied away by getting the Secretary of Defense job, but there's at least going to be remnants.
2) McCain, in 2000, said he "hates war." Now, obviously, he still recognizes that there are times when you have to act, but war might not be his first choice.
3) McCain was still very much a "maverick", just as prone to taking on Republicans as he was Democrats. He also had the whole "Straight Talk Express" going on. If he disagrees with either Bush or Cheney on how to handle Iraq, he may very well go straight to the people/press and explain his side.
4) In the early days, inexperienced Bush relied much on his cabinet...and Cheney and Rumself were long-time friends, dating back to when they were both in the WH under...was it Reagan? I could be wrong. So whichever of them came up with the Iraq War, the other one backed him to the President. Somehow, I don't see 2000 Maverick McCain being chummy with Cheney.
So...for better or worse, I think the world is a significantly different place ITL's 2008.