That's not the point, I know the center tank was NOT being used. But I doubt fuel was being pumped to the engines from the other tanks once the "explosion" took place. Therefore, no power for climb.
About 2 seconds.
An aircraft with an upward vector does not need power to climb. TWA 800 was climbing at the moment of the explosion and then the nose of the aircraft pitched up, giving it even more upward momentum. A climb of 1700 feet is not that significant in an aircraft traveling with the momentum of a 747.