I'm not an expert on this stuff, but I think you have it right. The signing bonus covers the years of control. The bonus is the players to keep, and then the player first gets league minimum, then eligible for arbitration, then eligible for free agency. Super-2 just speeds up when the player is eligible for arbitration.
here is a good starting point:http://en.wikipedia.org/wiki/Major_Leag ... rbitration
Also at http://baseball.blogdig.net/archives/ar ... Draft.html
scroll down to the signing draft pick section
Of course it is possible to sign a player at any time to a long term contract and extend the control based on the contract. (e.g. what TB did with Longoria.) But I don't remember that ever happening for a draftee, only for someone approaching or in arbitration years.