As it currently stands, the Big12 Championship game would be against Arizona State and Iowa State.
Both ASU and ISU are ranked below Tulane and Army who play for the AAC Championship. (Tulane's 2 losses are Kansas State and at Oklahoma)
So, feasibly, the AAC champion would get in as the 12-seed over the Big12 champion as it currently stands. Will see what happens when the rankings change because ASU will be moving up and Army will be moving down. Will be curious to see if they move ASU above Tulane.