Especialy if you do a 5v5 draft mode, if you are the last person to choose, after 2 bans, that's 11 champions that are verboten to you. If all of the free champs are chosen, and you either don't own any or they are already chosen/banned, you wouldn't be able to pick anybody.
Unless, of course, draft mode has a predefined list of characters you can choose from which is unique from the weekly frees and your own list of characters. I think that's the fairest way for that to happen. And it probably already IS, but I was just curious.