Look at the final rankings. I actually think it would have. Alabama ws .9419 and OSU was .9333. That is extremely close. That single game would have lowered Alabama in every single computer ranking and raised OSU in every single computer ranking. The computers look at strength of schedule and how your opponents perform. It would also impact human voting because people would have had slightly less respect for the SEC and slightly more for the Big XII.
I don't know if you still get bonus points for wins against the Top 10 but if you do, Arkansas would not be a top 10 team and Alabama also would have lost the bonus points.
I would really be interested to see a computer person write an article on it or run projections showing what happens based on that single game. The non-conference games are important. Another important non-conference game was ASU v Missouri. Missouri lost that game in OT. A Big XII win would have also helped OSU but not as much as the Big XII vs. SEC game would have.