It should but unfortunately, it doesn't work that way; not by Inno's definition. For them, it only works if that person logs in and the quest is up, then it checks to see if any progress was made. So if the GE was completed and closed, and the person logs in to get this quest, they will have to wait until Tuesday to complete the requirements of said quest. If the player logs in before GE was closed by the server, and the quest asking for such comes up, it will autocomplete. I had done GE-64 multiple times (even before the weekend comes) and had done many events with this quest that comes up. For me in Beta, midnight reset comes at 6pm local time. In Live, it comes at about 11pm local time, so I have some time to make sure this quest is done.