Based on my interpretation of the rules, the leaderboard can be set up after the initial submission on the due date for our game. Thus, as long as the game is functional, we can finish the HTTP stuff at a later date, if we are one of the top three games.

Is this right?

Yup, that's correct. However, you do need at least an offline score display in your game so players can compare their abilities.

The leaderboard takes about 30 minutes to set up. Maybe even less, so don't worry about it.