Yes and no. If your game require a lot of texture processing (Crysis and Battlefield series), then it will require more from your GPU.
But also some games require more CPU, like Don't Starve, Age of Empires and StarCraft, because there's a lot of units to control, rather then just fill the texture. It means, basically, if you have more CPU power, the game will run smoothly, with more FPS.
StarCraft 2, for exemple, is optimized in Intel's Core i processors, so you don't need a off-board GPU. But Diable 3 do require a off-board.