If you have 2 cards in SLI then yes you can run all 3 monitors (but probably not in games), if you have a single card then you can only run 2 monitors at a time, although you can have all 3 hooked up and switch between them.
The card is SLI compatible, but I don't have the second card. I will need to get the same type of card in order for it to work correctly, right? I can't put one kind of SLI compatible card in with a different kind, can I?
You are correct you can only SLI 2 of the same cards, but if your goal is just to run 3 different monitors and not to span games (which you probably can't do with your monitor setup anyways) then any ole NVidia card will do (you don't want to mix ATI and Nvidia because of driver issues).
Just to point out that nvidia dose have eyefinity, called "Vision Surround", also supports 3d gaming. Only catch is you need 2 cards for 4 screens and 3 cards for 6 and so on. Only supported in the new 4xx series and older 2xx I believe. http://www.nvidia.com/object/3d-vision-surround-technol...