The Driver it's self wont use to much processing power, but it could drive CPU use up if you update a driver and it improves game performance, allowing the game to use more GPU which means the CPU will have to do more work to feed the graphics card information.
That's the same with Dual graphics card set ups, GTA5 on one of my 780ti's, my 5820k was sitting around 40% CPU usage, Enabled the 2nd 780ti, CPU usage shot up to 60%, the more GPU power you have, the more information the CPU needs to feed the cards in DX11 or older.
DX12 will change how the CPU/GPU work with each other.