Are College Football Rankings Path-Dependent?

This is a question with a definite number-based answer, to be computed by someone with more time and who cares more about college football rankings. (As always if you run across this post and someone has already done this, let me know - mdcblogs@gmail.com.)

By this I mean: take team X and team Y. They start out ranked adjacent; they play a schedule of equal difficulty. Team X loses their first two games in a row and wins the rest. Team Y wins everything except loses the last two games. For both teams, they lose to teams of similar rankings; it's not like Team X gets upset by losers by Team Y loses to damn good teams. The only thing different about the two is when the losses happen.

I predict that Team Y will end up with a substantially higher ranking, even with all other variables equal, including their final record. The press and coaches will write off Team X after the first two losses, and even though they improve and fight their way through games for the rest of the year, they can't recover. Team Y has established their reputation and, since that's really what the coaches' and AP polls are about, they can coast for the last two games.

I don't have to convince too many people that the college football rankings system is stupid and dysfunctional, but this would be a nice quantitative proof of one aspect of that.