Even without the match scheduler, rivalries can totally happen. Mentors on 2815 (backed by the University of South Carolina) and 4452 (in the shadow of Clemson University) have traded a few friendly jabs this week and last year when they were with other teams up there. There may or may not have been a bounty for getting one of our "IT'S GREAT TO BE A GAMECOCK" bumper stickers on their robot (though nobody did it).
I suppose a on-field rivalry could be implied between us and 343. Set aside geography (they too are fairly close to Clemson) and our common ancestry (both teams have Donn Griffith at the top of the family tree), and you'll find we've crossed each other in eliminations there times in two seasons: Palmetto 2011 finals (1v4, we won), Peachtree 2012 quarterfinals (1v8, they won and ended up with silver), and Palmetto 2012 finals (2v8, we won). They put up a heck of a fight each time, but we'd just as gladly play with them!