There shouldn't be any problems. It'd be a serious anti-trust, class action lawsuit waiting to happen if one GPU/chipset company created problems with their competitor's products.
That being said, you do get advantages with running ATI VPUs on ATI chipsets and vice versa with Nvidia hardware. I'm not 100% sure what you ge when you match ATI with ATI, perhaps someone else can clear that up. But on the Nvidia 590 SLI chipset, running a 7900 class GPU activates what Nvidia calls Linkboost, OCing various clocks and buses by 25%. It does appear to mostly a gimmick though and not something you should base a purchasing decision on.
Lastly, I'm running an MSI K9N SLI based on the nForce 570 SLI chipset with an ATI Radeon X1900XT videocard without incident.