Never played a con game that didn't use pre-gens. Also never played a Hero System con-game, but I was able to answer the questions in general. As mechanically dense as Hero can be, well, as many RPGs can be, I would generally recommend bringing Pre-Gens if you are planning to run a game. (Especially with as broken as some Hero builds can be.) By using Pre-Gens, you can create stronger links to the challenges the PCs will face and ensure that the characters work well as a group. Whether they do or not, is still up to the players of course.
As someone who runs games for an indie game, Pre-Gens help me, it lowers the entry bar for new players, and because I know the characters I can help players jump into the action quickly, answering any questions along the way. Hero System being not that one game, the same logic probably still applies.