I can't figure out how or why the term "bottleneck" became so (seemingly) important to everybody. There will always be a "bottleneck" because there always be one component slower than the rest. If you fix it you will create another "bottleneck".
Yes and CPU bottlenecks don't usually matter much in games either. The CPU tends to only become the bottleneck when the GPU has minimal work. When this is the case, the frame rate is already so high that you don't care if it's 100 or 200.
The GPU bottleneck DOES matter though. This will determine whether your minimum frame rate is 30, 40, 50 or whatever. How far it dips sets the quality of your experience and the less dipping the better.
So, yes, you will record better benchmark scores with a fast i5 or i7. But in real life, the situations where a faster CPU outperforms a slower one are the situations you don't care about anyway.
No problem running a FX-8120 with a GTX680. It's a perfectly good match.
Whether a 670 or a 680 is a better choice is an interesting question. Personally, I bought my 680 before the 670 was released so never had the choice, but I don't regret it. Some people value smoothness and visual quality so highly that they're prepared to pay a lot extra just to eliminate a few lags and dips, or to crank up the settings one notch. That said, the 680 is quite a lot more costly than a 670 for what's on paper quite a small performance boost. Personal choice whether it's worth it really.