What do you mean?
How did Intel compete with ATI and nVidia? Same goes with AMD?
Up until now, it's been Intel versus AMD, and ATI versus nVidia. Now it's Intel versus AMD, and ATI (the video branch of AMD) versus nVidia.
If AMD wants to make it so that nVidia chips don't work well with AMD processors, then that's a fast track to cutting off huge chunks of your marketshare and filing for Chapter 11.
We didn't even see it with Intel chipsets back in the day when AMD made clone processors, as well as the K6 processors. And if there would have been a perfect time to do it, it would have been then!
I'm also not sure how feasible it is for the processor to behave differently with different video cards in. AFAIK it's more a chipset issue.