During the log-in phase and at the end where it says “Logging into game server”, the transition after that to character select plays some kind of click sound; it’s a common sound with AH and other interfaces.
It only happens to me on Classic Era and not WotLK or Retail. It only does it when starting the game up from the Battle.net launcher; going from character select, clicking Back, and then Reconnect doesn’t play the sound.