Being a primary school teacher who has sent many graduates to Langgymnasium, basically passing the exam guarantees a place at a public Gymnasium - but not in a particular Gymnasium. We have had some graduates shuffled from Rämibühl to Hohe Promenade, or vice versa, and there's always a chance of transfer after the two years ...
For Kurzgymnasium, I'm assuming they'd only transfer "excess" students to one with the same profile that you wanted.