No, you can turn off automatic alphabetization if you'd like.
After you have created your schedule, made any changes and saved the schedule:
1. Go to the File drop-down menu and chose "Export Schedule..."
2. Click on the Layout Settings tab on the upper left-hand side of the Export Schedule window that appears.
3. While in this tab, you will see a series of options with small boxes to the left of each option. Uncheck the "Alphabetize volunteers in (unnumbered) ministries by last name" option in that dialog. When you are done, the box should be clear.
4. When you export the schedule your volunteers will no longer appear in alphabetical order within the various ministries, and the distribution of each position in the ministry will instead appear in the order they do on the schedule in the Schedules pane.