Yes Huren, a similar feature could be added, maybe under the shoutbox. You could enter a challenge, select Classic or Free League, but you wouldn't be able to see who the other challengers are. Then the site would randomly put you together with an opponent.
The only doubt I have is, what are the odds of those games are going to be played? So for example, someone enters the challenge, gets an opponent, but he decides not to play against that particular opponent, avoids playing against that opponent. What would happen then?