Can Ubuntu split the desktop across two graphics cards?
Solution 1:
This should work fine, though I can't vouch for the stability of NVIDIA on Ubuntu. If you need another monitor, get an AMD card for it.
As long as your computer has the physical capacity for another PCI-E video card, you should be perfectly fine, and Ubuntu should recognize the second card and third monitor without a problem. Go ahead and get a video card when you need it and just make a new question if you have trouble getting it working.
Solution 2:
The answer is yes, it works. Nvidia drivers are fairly well supported, and this is possibly a duplicate question. You can find detailed how-tos on: How can I get xrandr to detect both nvidia cards: 2 x GTX480, triple-head?
And Enabling a triple-head (3 monitor) setup on Linux Mint 16 ("Petra") with two Nvidia cards
This should pretty much get you covered.
Solution 3:
There is no orderly generic way of making it work, nor a reference for deterministic diagnosis of what might be missing in a particular configuration, at least none supplied in any of the answers or available online. In that latter regard, it is utterly disappointing.
Maybe one day upgrading from 14.04 to a newer release, or newer Nvidia drivers would make it possible, but for now there's a myriad of layers of software and software settings involved, which provide little to no proper and relevant diagnostic information.
It might be the case that with Nvidia cards lacking SLI support this cannot work, but the current state of documentation leaves that at the state of a conjecture.