Every flight is treated as a stand alone movement - from ATC that is (which I am not). So, unless somebody amends the FPL or enter new estimated off block, then no.
One of the serious issues, when dealing with irregularities from the airlines' side, is telling the customers the flight is delayed. Some will be gone in an instant from the gate only to be seen again 10 minutes after the new, delayed departure time you declared so honestly.