It all depends, I have an i7 6700K, a GTX 980, and 16GB of DDR4 RAM. I run dual screens off the 980 and it's perfectly fine in terms of gaming even when playing videos on the other screen. It tends to be better using the onboard though, the 2nd screen video playback can get glitchy when running of the same card I'm gaming on. You're probably right regards game performance though, it's more the other tasks that run better when doing both.
My CPU never get's stressed enough to worry about and I don't notice the loss of system RAM either so for me those are not concerns.