The card would work fine, but the 6870 will run on its own. The 6870 is too powerful to use the hybrid Crossfire feature, so the graphics core on the A8 will be disabled. The fastest card that you can use for hybrid Crossfire with any of the Llano APUs is the HD 6670. Even then the 6870 will offer better performance than a 6670 with the A8 graphics core in hybrid Crossfire.
In my opinion I think it's pretty useless to have an APU with a 6870. Because APU's strength is in the graphics AND, you already have a decent graphics card which disables the APU's graphics. So, I think it's pretty useless and you can be better with something like i3-2100 or something like that.