Yes it definitely will. What is your current graphics card? Although the bottle neck will be there, you will still be able to play games at good FPS on that resolution. Dont expect cpu heavy games like gta4 and SC2 to show huge improvements but FPS shooters and other games should run just fine.
Ok, tell me first, are you planning a new system(CPU+mobo+ram) within 6 months? If yes, get the 6850. You can carry that over to the new build and it also has great CF scaling too. If not, get the 5750 or 5770. I think all the games you listed will work fine(i mean cpu will bottleneck the card, but overall the games will be playable at decent settings), apart from maybe BFBC. That game is indeed a CPU intensive one. SO, it all depends whether you will upgrade or not. GL.