Currently I am running an AMD Phenom(tm) II X4 955 Cpu, and a GTX 560 SE edition. I have a budget of 400$ so I can get a 3770k with a motherboard or possibly a GTX 670/Radeon HD 7970. If I do upgrade my Gpu will my cpu bottleneck it?
I feel with a mid line card you would be fine. Your GTX660/Ti and 7850/70 however the higher end cards may prove to be a bottleneck on your CPU. So its up to you really if you want to make the leap CPU wise you would need a new motherboard and CPU. Otherwise a new video card would just plug in play.
I think even if you do a healthy OC you are going to be pushing the limits of a HD 7970/ GTX 670. You will need a CPU/mobo upgrade anyway so I'd start there and then save up a little dough for a GPU. Like ndslite said micro center has the 3770k for $230 or the 3570K for $190 and tons of good mobo sales.
Here is my stock answer:
To help clarify your options, run these two tests:
a) Run your games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely cpu limited.
b) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 50%.
This will simulate what a lack of cpu power will do.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
set to 50% and see how you do.
If your FPS drops significantly, it is an indicator that your cpu is the limiting factor, and a cpu upgrade is in order.
It is possible that both tests are positive, indicating that you have a well balanced system, and both cpu and gpu need to be upgraded to get better gaming FPS.
If you are playing BF3 multiplayer, then you are likely to have a cpu problem.
In single player, thgraphics is more important.