You can always go to the ticket booth the evening before you plan to go to the parks and pick up your tickets then. That way you CAN go straight to the turnstiles.
If you buy your tickets from GAT and you plan to go to the Magic Morning on your first day, then it's really important that you pick up the tickets the day or night before. If you try to pick up your tickets at a DL ticket booth on a Magic Morning, you will quickly find out that the ticket booths open 30 minutes after MM starts.
I think I there was a thread a couple of months ago that mentioned you could pick up the GAT tickets from the "Will Call" booth. I did a search and couldn't find the thread. Is that the case?