Can I remove battery while my iPhone 4s is still on?
It should be possible to perform a reset of the phone by holding the 'home' and 'power' buttons for ten seconds. That should cause the phone to reboot.

If you can't do this (e.g. broken power button), then I don't see why removing the battery would not cause the phone to be shut down.

I don't see why it would cause any lasting damage, at any rate.