I use my iGPU when mining so I don't get screen lag or reduced hashrate.
If you also have a discrete GPU, my understanding is that you could use Mining Controller against that instance and mine on both!
I do use discrete graphics cards for mining. The display output source is set to the iGPU in the motherboard BIOS. I am unaware of CG/SGMiner of being to able mine with Intel iGPU or why I would even if it could.
So you have your monitor(s) connected to your onboard video card? That sounds like a good way to avoid the display lag if you didn't want to play games or otherwise leverage one of the discrete GPU's. In my situation, my primary desktop is used for gaming a fair amount, so using the onboard video card isn't really an option for me.