No that processor won't bottleneck that GPU. The definition of what bottlenecks a system gets really distorted. What is probably (and most likely is) slowing down your system is your primary hard drive. If you're looking to upgrade something add a nice SSD to your build like an OCZ Vector or a Samsung 840 Pro and you'll see things speed up significantly.
There is a big chance that you might experience FPS drops in certain CPU intensive games. Or another example - there are reports of some games running smoothly in single player with 50-60 FPS but they drop to around 30s in multiplayer. There was a recent article here at Tom's which compared Core2Duos and Core2Quads vs new Pentiums, I3s and an I5 dropped just for comparison. Core2Quad is still a very capable CPU, matching new I3s. If you have the money to upgrade go for an I5. Anything less is not going to make sense unless you want lower power usage. If you want to upgrade, I would suggest to wait a month and to go with Haswell, socket 1150. Anyway you can always overclock if you notice this frame drop, but for the most part it depends on the exact titles. If the titles you play are only GPU intensive. then there is no sense to upgrade.