No. It couldn't. Ole Miss and LSU were tied in the SEC at that point. Had LSU lost, LSU does not go to the SEC Championship game, LSU does not win the SEC, LSU does not go to a BCS game, they do not pass go, they do not collect $200 dollars.
Any other loss they still have a shot at the SEC and maybe (probably not, but theoretically) a shot at the NC. At the very least they get to a BCS game. Ole Miss also came within a hair's breadth of winning that game. I know. I was there.