Clock stops on a FD in college when the line judge sets the forward progress and waves his arms to the operator to suspend play. This happens at :01.
Relatedly, a stoppage on a FD play typically only lasts 8-10 seconds...would have been very difficult indeed to have run an offense off (particularly when WR's were instinctively running away from the LSU sideline immediately to assume an offensive formation for the next play) and a ST on before the start.
No guarantee even if they had that they wouldn't have committed a game ending penalty in the hubub for too many men, procedure, etc. And then no guarantee that it wouldn't have been blocked (see Bama v Tenn, OM v Florida, etc) or missed.
Of course, if you're LSU you might just feel lucky enough to have had the chance- after 2 OM TD's erased due to penalties and a poor call, a blocked FG returned for an LSU TD, a botched scoop and score by Cornell that would have iced the game, completing a Hail Mary on 4th and 26 just to have this 'debate'...........