The issue I see with this is that there would be thousands upon thousands of entries, with a huge number probably being low quality. This Board is evidence of that to an extent. So many half-baked champion ideas and paper kits with no soul. :/
For that reason, I would assume that the contest would be art-based, with kit and lore being secondary. It probably wouldn't be just paintings or drawings either. I could see them letting people do cosplays, clay models, 3D models, etc. etc. whatever they needed to do to visually communicate the flavor and theme and personality of the would-be champion.
The majority of champions who've made it into the game started off as a Riot concept artist just doing their thing.