Would using a single CUII card negatively affect the graphics quality in any significant way when using 3 monitors?
Well, the 7970 has 3 gigabyte of vram, which is enough to run Battlefield 3 on high with some AA and still get 30+ fps on average. So, I guess the tiny bit less performance would weigh out any trouble regarding a CrossfireX setup.
Also for advising that with one card there would not be any microstuttering, and when correctly set up using Displayport to Displayport there would be no tearing.
This thread covers microstuttering, so I would highly recommend looking around there. There is always the chance that you won't get microstuttering, but the odds are high. However, I believe they found a fix of some sort. I'm not yet fully informed about the stuttering problems, so you should check that thread out before you believe me ;)
Moose