Your thinking about bottlenecking in a weird way. You just have to understand it...how to explain?
But it doesn't matter anyway, since your limited to the PC you have. Sure you could get a Radeon 2400 pro, it's over 30 times weaker(graphically) than a 7770 and uses only 20 watts. Your system wouldn't bottleneck it, but it would be useless. You have to get a GPU your system will bottleneck. At least with a 7770 you'll be ble to play some games. You could run a 7970 GHz edition if you wanted too.
Ya, an Asus RoG board with an i7-2700K screaming at 5.2GHz would be great. And you could easily get 100% out of anything, including crossfire or whatever. But there is a money thing.
Here is guy with a 4800+ and 7770. Many games are so GPU dependant, bottlenecking - even with an old CPU is minimal.http://www.youtube.com/watch?v=P21T2gCBkqY