all but the very biggest of programs. Most P5 programs don't even have a realistic shot. They have to go undefeated AND schools like Alabama and Clemson have to have more than one loss.
They will always invite a one loss Alabama over an undefeated Utah or Arizona. There's too much money at stake not to.
The cold reality is that even a top 4 BYU or Cincinnati will never get serious consideration for a playoff spot. That would certainly undermine its legitimacy, but the playoff system is strong enough to take an occasional credibility hit. It would require several years of obvious unfairness to force a change for the better.