Does Sata 3 make a difference over Sata2 for gaming?

NO.

If you havd a SSD for loading levels, then sata 3 and a suitably capable ssd might load the levels faster.
6gb hard drives would make no difference.

As to FPS, there is no connection.

If you are thinking pcie 2.0 or 3.0, the answer is still mostly no.
Only with very high end graphics cards and only in benchmarks can you tell a difference in fps which is only perhaps 1-3.