The battery is attached to the back plate of the iPhone using adhesives you know? Glue. Soldering isn't even an option considering the back plate of a 3GS is plastic. For future reference, removing a screen (both digitizer and LCD.) while on will have no effect. You just can't use the iPhone (duh). Though, you can flick the switch on top of the volume buttons that make the iPhone go *vroom vroom* on and it will work.
Yes i know that, i have replaced screens and stuff before, but the thread title should have been screen not batery. as you are not removeing the battery; you are just unsticking it from the back plate. And yes, the device will work fine without a screen and or digitiser. It will also shutdown and boot up fine without them. which could also make it into a useful headless server. like a raspberry pi. (The only reason you would do this would be to save the small amount of power the screen/digitiser uses.)
I thank you for your advice but none of that is what I was looking for. I have also come to realize that it's virtually impossible to remove the battery while the iPhone is running because the battery is under the motherboard.
Well, you unhook the pin from the mother board before unscrewing the motherboard, so technically you removed it while it was on.