Well, the games you mention will "run"; how well is questionable?
For future reference, you have an HD 4570, which meets the minimum requirements of the games you listed, but, know in advance that it's a budget/low end card, so high settings are not going to be an option with new titles.
Also, you know how it goes with that whole, "game experience may change" clause that developers are fond of... patches usually bring greater demands.
I can tell you that Bad Company 2 is more demanding than when first released, which is making dual core guys none too happy.