There is no advantage.
The offers come in by day, not by time. A better offer could have been submitted before your "best" offer.
The "current offers" you see on the player card are the offers as of "yesterday" in sim world. Any offers then made that day do not update the player card until the next day.
*** EDIT
I just realized you were talking about a coach. I don't know if where (if anywhere) current offers are shown, but the same principal would apply.
Last edited at 10/31/2015 4:04 pm