It should run those games just fine, aslong as your CPU is decent. If it makes you feel better I run a 9800GTX+ on my 50" plazma (1920x1080), and it runs everything better than I could expect!
I play L4D, black ops, Assins creed 2, alian swarm, ect. Max resolution, 8-16x AA, and all the other settings maxed out. Although I do offload physix to the CPU (quad core q9400 @ 2.5 Ghz), so that helps. I would highly recommend downloading the EVGA Precision utility and set up the Auto Fan control, which works wonderfully, it keeps my GPU at a decent temp!
It isn't the physical size of the display that makes a difference in performance, rather it is the number of pixels you are manipulating. Whether a 27.5 inch monitor or a 50 inch HDTV, 1920x1080 on either is the same number of pixels.
BTW, the 470 will perform great at 1920x1200. Good luck!