I've heard of a few cases of people going through hell and high water trying to get both of them to work simultaneously (mostly due to driver issues), and, in my experiences, using one graphics card for actual graphics and using another graphics card by another manufacturer for something unrelated to displaying an output on the screen (such as for brute forcing or mining for bitcoins) doesn't severely impact regular operation. While I haven't tried to get both graphics cards working in tandem for specific graphical purposes, I would very much advise against trying to get two different cards from separate manufacturers to display graphics to the same screen simultaneously. In my honest opinion, that'd be begging for a bad time filled with driver issues and headaches.
Then again, my only experiences with this sort of scenario (two different graphics cards in tandem) have been only using one of them for graphics, and my only source for any definitive advice against your proposed setup are third-party stories and trying to reason out how that setup would be possible without finicky 3rd party software.
In short: I wouldn't risk it—I'd do a few benchmarks with both cards and see which one fits my needs best. Regardless of which route you choose to take, I hope I was able to provide some insight into the issue.
Edited by cryoganix, 29 December 2013 - 12:06 PM.