Can my setup run Bad Company 2 smoothly?

With that graphics card, you'll probably only be able to run it at low resolutions; it's not really that great. But I don't know what Jim was saying about the i3 processor being rubbish; it's a 32nm 2.93GHz dual core processor. It should be great for gaming. 4 gigs of DDR3 is still more than enough, it should be fine for BC2.