Looking at the title of this thread, I started thinking about a different (and unthinkable?) scenario being discussed, similar to the co-op bridge in 2012. Glad we're not discussing it, and I hope the discussion is never needed.
Back in 2008 there weren't enough game pieces to go around. There were certain teams (like mine

) that picked a wrong strategy for the game and ended up building a sub-par robot. During regional competitions, it was a rare occurrence to be paired with two robots that were significantly better than average. This meant that the best robot got a ball, and the other two shared.
During the championship event, it was a rare enough occurrence to have two below average robots on an alliance. Ultimately, teams like mine tended to be deferential to the other two - which is to say that we didn't go after a game piece until we were told we should by another team.
From experience, I can say that there will be plenty of opportunities to demonstrate your abilities. My team catapulted the trackball several times that season. If you don't think your robot is good enough to pick or be picked in the first round, your offensive abilities likely won't be the only reason you would get picked for elimination. One thing that is guaranteed is those picking will remember uncooperative teams and bad attitudes. If you do your best to be a team player, you will do better than you would otherwise do.