No - remember that OT in college football is based on alternate possessions, not on scoring.
Since each team will get a possession, the team that plays defense first gains an edge in the alternate possession. If your opponent scores a TD, you know that you need a TD to extend OT to another set of alternate possessions (or get a TD + 2 pt to win). If your opponent makes a FG, then you know that a FG ties it and a TD wins it. If you stop your opponent from scoring, then you gain an almost insurmountable advantage, as you now go on offense with only 25 yards between you and victory.
As such, they always give each team a chance to play defense first. If it goes to a third OT, they flip a coin again and restart the sequence. Starting on the third OT, teams must attempt a 2 pt conversion if they score a TD.