Technically i have no idea but would have thought it very minimal at most. There was a post last week that said turning off Audio over HDMI would give a small boost and i guess that anything the GPU isnt doing extra can only help but i wouldnt go to those lengths myself.
Ati used to make an All In Wonder GPU, This was basically the model of GPU with a TV tunner onboard with some codecs etc, These cards didnt show any performance differances worth noting. Single Frames at most from what benchmarks i can remember seeing.
Run an intensive benchmark with it installed and without. I'd be surprised if there was any difference. It probably also depends on whether you use XP or Vista/Win7. My guess is it would be very, very minor.