I used the notebook version of the 6570 for awhile. My screen defaults at 1600 by 900 and I frequently pushed high settings.
Now granted, I didn't buy Skyrim or the Witcher 2 until after upgraded to the 6770M (also mobile).
But if your only planning on pushing 1024 x 768 I don't see why a desktop gpu couldn't handle them.
That said, I'm a little concerned about any sort of Celeron or Pentium branded part.
My laptop used an Intel Core i7-2720QM, so I was purely limited by the system's GPU
You could be CPU limited, but you may still be fine if it meets or exceeds the game's recommended clock speed and core count (not just the minimum requirements)
Dunno why you are concerned, it is sandy bridge after all. The $70 pentium g630 is better than FX 8120 in gaming. And the celerod g530 so it is the best CPU for under 50$.I have seen videos on youtube with celeron g530 paired with hd 6750 playing battlefield 3 on high and skyrim on ultra so i should be ok with celeron.
But i m concerned about GDDR3 memory on the HD 6570, as i can't find gddr5 hd 6570.