No but in a gaming PC it's the GPU that matters. Phenom II X4 965 is enough to drive the 7870 (my Phenom II X4 955 is clocked at 4 GHz and It drives two 5850 without bottleneck).
If you can have both FX 6300 and 7870 great, go for it! If you can't I would prefer 965 + 7870 than FX 6300 + 7850! BF3 is GPU intensive so as long as your CPU doesn't bottleneck your GPU you aim for the best GPU! Also CPU cores help at these game so a Quad Core and a good GPU is just what you need for that budget!