Previous Answer: An iphone is like any other phone. so no.My Answer:It is arguable that an iPhone is not list any other phone. However, that is not the issue at hand. The issue at hand is, "can you play on an iPod touch while charging."
The answer is yes.
Unless you are using add-on equipment, to charge an iPhone/iPod, merely plug the iPhone/iPod's cable into a USB port on your computer. Usually, iTunes will start and your iPod will begin to charge.
Here is the important part: you may now use your iPhone/iPod as you normally would except for the fact that is no longer "portable" as the device is now plugged into a computer's USB port.