Doesn't appear to be possible. A quick press of the power button on my ACD puts the whole Powermac G4 to sleep, not just the display. So it's a whole-system sleep button, not a display-only sleep/power button and it's computer on = display on if it's drawing power from the Mac's ADC/AGP port.
If you're running it off a Mac Pro or G5 though (as it appears from your pic) using an ADC/DVI adapter, your on-off switch can be the wall socket switch. And the sleep/power button is disabled anyway - the ACD I have running off my G5 via an ADC/DVI adapter does nothing when I press its power button so I'm guessing that's the same case with yours, although the display preferences button does work as normally.