No. It applies only to people under a certain age, and it only applies if the player wants to go to play in the MLS. The drafted player is free to go to Europe or anywhere else if they want.
Within the league though, if Toronto drafts a certain player, then that player can only sign with Toronto until another team trades for his rights or he reaches a certain age and his rights expire. It's the same system used by the NFL, NHL and NBA. North American sports fans are used to this system. As the league grows and improves, I expect them to switch to the way everyone else does it.