Yes, you can do that. I have run my old system w/ an ati 9700pro that way. I have never run the taskbar across the monitors like that but that is a windows thing, not a graphics card thing. If the card is cabable of multi-monitors (which all modern cards are) then the OS is the one that actually does it, so you are fine.
One caveat is that you say you ran one game on both monitors. afaik that is not a standard ability. (windows defaults the game to a "primary" monitor) Perhaps your Nv card came w/ some 3rd party app to enable it to spread over both monitors? Matrox has cards that do it, and they also have add on devices that allow other cards to do it. But beyond that the game must support it otherwise you need one of matrox's devices that "trick" the system into running one "large" monitor at the resolution of both of your physical monitors combined (2560 x 1024 for example). If you say that you did it then I believe you, I have just never seen it done that way outside of some of matrox's work.
Again, this is getting beyond anything I personally have done. Could be that I am over-thinking it and it is something simple. Just trying to offer the knowledge that I have, and I have been wrong before.
I know the theGreatGrapeApe would have a better answer... where is he anyway? This is exactly the kind of post he would normally get in on.