Does a black screen save battery on an iPhone 4?
Yes - brightness is the major thing you can change to save power if the screen is prevented from dimming. Having the screen off entirely significantly extends the runtime of the battery across the iOS platform.



I haven't found a good reference to determine if the natural state of the IPS transistors that control whether the pixel is open (colored) or closed (blocking or black) but the amount of power needed to activate all of the transistors and let all the backlight through is certainly dwarfed by the amount of power needed to run the backlight itself.

Since the backlight is dimmable, it could be more of a factor when the backlight is set at the lowest light level, but I would expect the actual panel itself to still be negligible compared to the backlight (and more importantly negligible compared to the CPU / GPU and radio power usage)



If you take a look at the official specs you can see for the iPhone 4S:


6 hours: 3G Internet - screen on all the time
8 hours: 3G Calling - screen off most of the time
9 hours: WiFi Internet - screen on all the time
10 hours: Video Playback - screen on all the time
40 hours: Audio Playback - screen off most of the time


It would be interesting to see how long the audio playback test would last if you had a simple app to keep the screen on the entire time...