Non-BCS teams and the national championship

Can a non-BCS team win the national championship?
That’s a question Rivals.com writer Olin Buchanan tackled recently. Mountain West Conference commissioner Craig Thompson told Buchanan it is possible.
“I think we could play for a national championship,” Thompson said. “But it would take a couple of factors. We’ve had five teams in nine years go undefeated in conference play. That’s the first absolute ‘ you have to go undefeated. We’ve had only one team in nine years go undefeated in conference and non-conference ‘ Utah in 2004. So, you’ve got to be 8-and-0 in conference, undefeated in non-conference and also dependent on playing good people like Texas A&M and North Carolina (which Utah did in ’04) and some teams that could be ranked high. Lastly, you’ve got to have a little bit of luck. The year Utah was undefeated, so were Auburn and two others.”
Here’s what Buchanan wrote about the prospects of a non-BCS school vying for a BCS bowl game in 2008:
‘… the teams that seem most likely to crash the BCS party this season would be BYU of the Mountain West and Fresno State of the Western Athletic Conference, with the MWC’s TCU and Utah and the WAC’s Boise State also capable of making things interesting. BYU has more cachet than perhaps any other non-Big Six team because it won a national championship in 1984 and has a history of knocking off respected programs, including UCLA and Oregon in bowl games the past two seasons. The Cougars haven’t lost a conference game in two years, and this season face Washington and UCLA in non-conference play.’
It’s difficult as it is for a non-BCS team to qualify for a BCS bowl. Do you think a non-BCS school will ever play for, or win, a national championship?