I doubt it, and even if you could I don't think you'd see a performance advantage.
NVidia's NVENC solution for example, samples the OUTPUT of the video card being used and sacrifices a few processing cycles to do that, but it's pretty efficient as it's being put through a dedicated encoder.
If the AMD card had that (does it?) it would make the most sense to use the main card likely. I just don't see taking the video signal, sending it back to the main bus to the second card to be processed.
I could be wrong.
Anyway, I think you have to investigate all the main solutions but I think you're limited to Intel's hardware method, or software (again CPU): http://video-game-recorder-software-review.toptenreviews.com/
If AMD has a method to actually use the graphics card efficiently I can't find it.