Bottleneck is a term I do not much like. It implies that somehow you will get reduced performance with the upgrade.
In truth, upgradeing to a GTX580 will improve your fps and improve your minimum frame rates. The only question is, by how much.
If your games are multi core enabled, (which is why you picked a 6 core amd cpu over an ivy bridge cpu in the first place) , then you will do better than you think.
If your games use the typical 2/3 cores, then you may want to rethink the amd cpu for gaming.