dangus :
yes please upgrade to 6700k plz.
It absolutely will not bottleneck, a 3570k with a bit of overclock is equivelent to a 4690k which is still brand new selling, current high end gaming CPU which in itself is close to the 6600k also.
You will be totally fine. It will handle any GPU, it still has 4 quite fast cores. A 2nd gen not overclocked might see some loss in performance. But not a 3570k