Just as an update: in spite of the delay until I received the conditional acceptance letter on the website, I ended up not even needing it. They never asked to see it even once. I arrived to my appt at noon, 45 min early (surprisingly no traffic), I was done before 12.30. They took my passport and drivers license, called me back for the usual rigmarole and done. Said I should receive the email within 48h (I had the email by 2pm).