Nope, there would be no bottlenecking.
I find this generation difficult with giving recommendations...from the start the GTX 680 is overall a higher performing card. Its also quieter and draws less power, but is a tad hotter at load. It even beats the 7970 at 2560x1600 quite a bit.
The 7970 has 3GB of VRAM compared to, and should realistically perform better at higher resolutions. It has no issues with computations, unlike the 680 (ignore this if you don't do computational workloads). The 7970 can also achieve a better overclock and at least level the playing field or surpass the 680.
If you require the use of a computationally strong card, the 7970 is my recommendation. If you simply want a stock card, and no factory overclocking, nor your own, I'd suggest the 680.
All in all though, I'd go with the 7970 in this situation. Specifically, the GHz. Edition, especially for that price http://www.amazon.com/XFX-Radeon-D
[...] s=xfx+7970 Due to the factory overclock, rather high too since it OC's very well, they got a lot of performance out of it and the 680 doesn't fare as well against it. Even "Superclocked" editions come relatively close, but don't surpass in most cases. It will perform hotter, draw more power, and run louder however.