the game should perform fine. You probalby won't be able to use AA, though.
The 3870 X2 is probably on the level of a GTS250 or maybe 4850. That's enough for Warhead, but you may not be able to use anti-aliasing at really high resolutions.
I'd say the weakest link is the graphics card. It's not really weak, but the new ATI cards are leagues above it (they really improved with the 4xxx series).
The CPU is fine. Clock speed is a little low; I bet you could just clock it up a little for free, though. I don't think it's going to stand in the way of much of anything as is, though.