Actually that 6870 is perfect for that resolution. You should see decent framerates.
it should be a lot better than decent though it depends on how you would consider as decent. for me having more than 30fps at all times considered as decent. with his setup he should get more than 60fps in majority of games except a few that was intended to make gpu cry even just to get 30fps (metro 2033, the witcher 2)
So, a resolution of 1680 X 1050 have better chance of displaying games at High Settings than at 1920 x 1080 since it's less demanding on the GPU?