The thing is, If you intend to game at 1080p (which you most probably will after buying that LED) the CPU and GPU will both work in coordination and there will be lesser bottleneck as compared to playing at 1024x768 or something similar. To make it clear, let's take an example -
Now, you're playing BF3 at 1024x768 at Ultra settings. The GPU (HD7850) is capable of delivering around say 100 FPS. BUT, your CPU is weak as it can't process the requests sent by the GPU to calculate game data needed to provide 100FPS. So, due to bottleneck, you will only receive around say 70 FPS at that resolution.
Now, let's say you're playing BF3 at 1080p at Ultra settings. The GPU can deliver around 45 FPS at that settings. Also, the CPU is good enough to calculate the game data needed to provide 45 FPS at that settings. So you will get full 45 FPS at high resolution as there will be no or negligible bottleneck.
Even if it bottlenecks the GPU at 1080p, mild overclocking will sure do the job. Go for Hyper 212 Evo as it is slightly better at cooling than it's younger brother TX3 and is only 1k more than TX3.
Also, get MSI/Sapphire HD7850 2GB card. Forget about GTX560Ti now. 7850 is much better overclocker, runs a lot cooler, is more silent and takes up very less power (in the range of a low/mid end GPUs) and still provides decent performance over GTX560Ti in many games.