I think it is a big deal and can make all the difference in a competition. My coach drills it into us before every competition. One problem though, the "fight" for the center spot, can only be won against dancers from other teams. :-)
on a similar matter...
My Latin partner and I often dance with closed eyes-- though not at the same time... Specifically when we are getting tensed because of a new or fast move.
I tend to follow better with my eyes closed and I have better connection. I concentrate only on his lead and...
Competition - position on the floor
For Latin, I like the middle of the floor
Light is often better and one is more in the judges view.
For most of the comps I have danced, they are not walking around.