It does with my 7850, when I upgraded from the 6870 I noticed no difference at all in any of the games I play. My CPU is OC'd about 400mhz or so, pretty light but still god aweful slow.
I would say no, but you can find out yourself by running a simple test.
Run 3dmark and note graphics score. Then overclock the cpu 300mhz and run the test again. If your graphics score went up, then you know the cpu is holding you back.