If what is happening on the second screen requires effort on the part of the GPU (YouTube, website with lots of flashy add), you might notice a difference - especially if your card defaults to "playing video" clocks rather than "gaming" clocks by mistake.
If you're just having the second screen sat at desktop, or something that doesn't need horsepower such as Notepad, then you'll notice no difference at all. I've tried my fourth screen on my GPU and on my Intel onboard, and there was no noticeable difference in games. It's a bit like having a passenger in your Ferrari during a racetrack lap - technically it'll be slower than without, but you'd need very precise measurements to actually find it.