Yeah it'll work, but it only has one PCI-E power cord, so you'll need to use a molex -> pci-e power cable.
Edited:
As for the FPS problems, sounds like something may be overheating, run a temperature monitoring program (HW Monitor) while you play, and after a while check the max temperatures. If that doesn't seem to be the problem, it might be something else like HDD being accessed, page file usuage, etc. How much RAM do you have? And are you currently using the 6870? It should be fine with a CX 430.
I AM using the 6870 as of now, and I applied thermal paste before I sandwiched the fucker of a cooling fan onto the processor. I have 4 gigabytes of RAM which seems sufficient, but I'm not sure. I also think that something might be related because I flashed before I put the processor in, but I don't think flashing my mobo again would work, and I think it would brick it.