Both nvidia and ati have their own ways of handling dual-screens. I see no reason why the kernel would not support two video drivers simultaneously; however i doubt you'll get them to play nice.
I suspect you'll end up with each screen gaining its own x-server. Essentially this means you'll be running two full desktops off the same computer, i.e. you won't be able to interact between the two monitors.
Investigate xinaramma, which is X's (not the more device dependent ati/nvidia) way of handling these situations. Its possible that with this you can unify your desktops.
In short, there shouldn't be any issues if you just plug in your card and see (although connecting the hardware might be a challenge depending on the ammount of power/motherboard connectors you have spare,) but I expect you'll have to do some manual configuration to come to the solution you want.