Dance competitions tend to be long and involved - kids don't have a lot of free time during the competition - so the parks shouldn't feel any effect during the day of a competition. But at night, or the day after the competition is over, depending on the size of the competition, it could be busier than usual. Of course, there is always something going on at WDW - conventions, sporting events, competitions, so one competition isn't going to affect it too much, IMO.
We just participated in a sold-out dance convention in Boston, at the same time a high school mock U.N. was being held in the same facility. Now that was crowded!