CS isn't a graphic demanding game but CS GO is a bit.5670 is a good choice.don't play with overclocks.your psu is holding you back.anything above 5670 or 6670 will face bottlenecks from your cpu.
No it won't your CPU is going to hold you back. Even on low res and settings on low. You should get about mid 30's or 40's. You would need a bigger CPU and a GPU.