That video card is overpriced.
A 5670 performs better and costs the same.
Or you can get a 4850 for ~$90, which performs much better than the 4670 (also better than the 5670).
It should work for the computer (1x PCIe x16 slot), but the problem is you don't know what PSU it has. It will run a 4670 or 5670 fine, but you won't be able to upgrade it much in the future.
Long story short, yes it will work. But consider building your own computer with parts from newegg, or going to vigoor, digitalstorm, cyberpower, etc where you can pick out your own parts.