A non-power conference school would have to be really fortunate to make the playoff. Look at the 2004 and 2008 Utah teams, which were arguably the two best non-power conference teams that I can recall, and neither of those teams finished in the top 4, even after the bowl games. The MWC was pretty good in those years, and those teams also had some power conference non-con games, including Michigan in 2008 (obviously that was Michigan's worst year in a long time but that's besides the point).
The fact that UCF has a 25 game winning streak and still can't get above 6th (and that was only after last year's bowl win), is telling. Part of that is bad luck that cancelled their games against Georgia Tech and North Carolina the past 2 years, though, not that either of those teams were good.
2010 TCU (before they joined the Big 12) did make the top 4 before the bowl games, but that was after going 11-2 and 12-1 the previous two years, and (not that this should matter) they had more historical credibility being a long-time SWC program with some great teams....