Not any time. When Ohio State and and Clemson beat them in the playoffs they cared.
But the ones I mentioned when they came up a game short of making the BCS NC it was obvious they didn’t care to be playing in the Sugar Bowl.
TN has done it before too. Like the year we were #6 and got a BCS Bowl snub and ended up in the Peach Bowl. It was obvious the players didn’t give their all that day.