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I never heard about tournament games counting regardless, but i guess it could be.
Yes, a "rated" game will not be rated if it is deleted, timed-out, etc after less than 2 moves from each player (4 moves total). This also allows players to delete a game they didn't want to play without being penalized. (For example, if someone accepted their Open Invitation whom they didn't want to play).
(hide) If you want to always be warned about the latest post on a discussion board, you can receive the posts on your news client by clicking the RSS logo at the top right of each board. (pauloaguia) (show all tips)