OLED displays are made up of tiny organic LEDs (light-emitting diodes), so each subpixel emits its own light - the display is black when they're off. Different amounts of light emitted from the different colour subpixels gives a pixel with an overall colour. So if only 9 pixels are lit, only those 9 pixels are consuming power. This also means that brighter and whiter images use more power.
This is in contrast to a LCD, where there's a backlight that makes the entire display white when all the subpixels are off. Liquid crystal subpixels block the light to varying degrees in order to produce the image; each subpixel has a red, green or blue filter to produce colour. Therefore the image is subtractive from a white background. The power consumption doesn't really vary depending on the image being displayed, because the backlight is always on over the whole screen.
However, I don't know if the CPU would be able to sleep with the display "on", even if the display itself isn't consuming much power.