In general, I wouldn't do it that way.
I doubt there is any noticeable CPU difference if having a basic screen, but running a web browser or other taxing program is going to increase CPU usage, video memory and system memory usage regardless of how they are setup.
If you had very limited system or video memory then one choice might be better than the other but in my experience I tend to use the same GPU.
(for example, if the iGPU is set to use 1GB of memory which will be your DDR3/4 memory likely that's really a waste on a secondary monitor especially if you only had 4GB of system memory... which means you only have 3GB left...drawing to a secondary monitor the iGPU might only use 40MB or so normally)