Unless the new 24" supports that standard, you'll have to use Firewire 400 (assuming that the drive supports it). My ACD 30" has two Firewire 400 ports and two USB ports.
In any case if the drive and display both have similar ports (both with Firewire 400, both with Firewire 800 or both with USB 2.0), then you should be able to plug the drive into the back of the display and it should work. All ports on the ACD are powered, whether the computer is sleeping or not.