Our quads are roughly the same, and until 2 weeks ago I was using a 9600 GT.
With the 560 I notice cpu bottlenecks only in the very high end dual core games.
This is also due to the high res I play at.
However, for the quad core games you'll enjoy the massive performance increase.
On my Athlon X2 4200 with my 9600 GT I averaged 15 fps in BC2 on medium settings, still unplayable, the simple quad-core upgrade nearly tripled performance on higher settings, then the 560 allowed me to literally play at 1920x1080, 4x AA, 8x anisotropic, Vsync on, and I average 60 fps, I occasionally go down to 55 with lots of explosions. <-- not an exaggeration, I monitor it every time I play, now I'm hooked on the game.
But there is no universal bottleneck or not, your bottleneck is/will only be relative to many things that concern only you and the software you're using. Even where I was already bottlenecked by my 9600 in Crysis, the upgrade to the 560 significantly improved performance so with the new settings I play at my cpu is once again the bottleneck. The performance will vary based on what you do and what you play.
So in other words, your processor being a bottleneck varies upon the resolution, game's optimization, and other factors.
All in all, you wouldn't be wasting money on a 560 and it'll be amazing for the quad core games and most dual core games, I'm enjoying mine.