No, I don't that be somewhat true, I ran minecraft in my laptop, it has I think the nvidia 315M GPU and it ran minecraft on far/fancy at the average 60fps and won't dip below 50. It has the i5 arandale (whatever) CPU with HD graphics, and since my laptop has optimus switchable graphics, I can switch my GPU to the HD graphics. And all I get is lag, like 10fps that is used to be 60fps.
But could be CPU bound too, dunno much.
i'm not saying that the game ONLY uses the CPU, i'm saying that the CPU is what cause more FPS difference, but if you are only using CPU of course there will be more lag than using any dedicated gpu to help...
but if you have a mid-low end gpu the game will already run good and changing it will almost not improve performance.
on the other hand, if you have the same graphics card and upgrade from a dual core cpu, and go with a i5, you will notice the difference.