I would like to know if a corsair cx600 will be enough to handle a single GTX 570
The rest of my system:
Intel Core I5-2500k
Asrock Z68 Extreme3 Gen3
Corsair CX600
HAF 912
8gb ddr3-1333mhz
Seagate-500gb HDD-7200rpm SATA
Go with Tx or Hx series they are much better and reliable.Though your cx series is not at all bad but after few months can lend you into trouble after all you are using a 500series card.
I won't recommend you Ax series because that is not required.