Yes, battery is consumed faster when using the GPU - I cannot tell you by how much, but obviously it is enough on iOS devices for Apple to change its feature sets there.
Can you give a citation or backing research? In my experience, if you've got two similar operations, the one on the GPU will consume less power (assuming you don't need to transfer substantially more data over the bus).
i'm not an hardware expert, so I cannot tell you excactly how it works, but the point is: The device will calculate the same result in shorter time -> from what I know: If you want to calculate faster, you need more energy
Also I don't think the devices are built to supply the CPU with less power while using the GPU.
Again: these are mostly assumptions, I'm not a hardware architect!
But for doing graphic manipulations, wouldn't it make sense that the net energy used by the GPU getting them done should be less than with the CPU?
I guess that also depends on how efficiently the GPU is used.