No, you cannot. nVidia cards are limited to driving 2 independent displays per master GPU. When you enable SLI, one GPU becomes a slave to the other, and is no longer capable of driving independent displays.
With SLI disabled, you can power/drive all four monitors just fine.
If you enable SLI however, two will be shut off. You can get one to turn back on if you set the cards to run the monitors in Surround 2D or Surround 3D, but then you lose the benefits of them being separate monitors - windows simply sees the setup as one triple-wide monitor - one independent display (but built off of three linked displays).
There's little reason to get two different cards - If you're not going to run SLI, might as well keep things simple and get two of the same. Then you can always SLI if you need that additional power for something.
What you can do, and I did until one of my cards died, is run 3 graphics cards, two the same, and one different. You can SLI the two similar cards, and use those to power two of the monitors, and then drive the remaining two monitors off of the third card. Because the third card is different & unable to SLI with the first two, it will not have any of its outputs turned off when you enable SLI. It doesn't even have to be an expensive one, unless you plan to run fullscreen applications on the monitors connected to it. I used a $25 card since I only used the monitors for webbrowsing / chat windows or similar, and you can drag windowed games onto the auxiliary monitors and they'll continue to run with SLI since that's all rendered off-screen and composited into place in most of today's operating systems.
You can also look into AMD cards, as they are capable of driving up to 6 displays off of a single GPU (provided correct connectors, usually you'll need a monitor with DisplayPort, or an adapter to convert from DisplayPort to what your monitor can accept), but I'm afraid my knowledge there isn't quite as extensive.
This answer is slightly out of date now. The GTX680 and later cards can drive up to 4 independent displays off of a single GPU, though I think it will only do 3 of the monitors in a nVidia Surround setup; the fourth is limited to being an auxiliary monitor, typical of a "3+1" setup.
I managed to use two ports from my motherboard. DVI and analog. Asrock Extreme 3 Gen 3. – Valamas – 2015-01-19T06:20:36.417