As au_equus stated VRAM is not additive, you're still limited by the VRAM bandwidth of the primary card (2GB in this case). What 750W power supply do you have? a quality one will suffice but a cheap PSU may not. I cant speak for what FPS you could get on Crysis 3 but you may be able to unlock (depending when you bought the card(s)) the 6970 shaders giving you better than a 6990 in performance (in CF).
Does eyefinity matter? well of course, your pumping out 3 times the pixel rate, thus you need ~ 3 times the graphics power to get the same FPS as a single monitor set up (a simplified assumption). I run Eyefinity @ 6048x1080 with essentially 3 x 6970's and I don't plan on being able to run Crysis 3 on High (I like to maintain around 55-60FPS).
So in full, yes crossfire works, you can expect around a 80% increase in FPS (that's conservative, and only for the first CF card, the second and third see diminishing returns) but your eyefinity setup will take allot of GPU power, Medium settings may be the best you will get with a decent frame rate.
Here is an article comparing many cards on Crysis 3 :
http://www.guru3d.com/articles_pages/crysis_3_graphics_performance_review_benchmark,1.html
as you can see even 1 6950 on only a single monitor gives a less than playable framerate although it is on High settings. Read from that what you can. Hope that helps.