The employees in my unit are used to having flexibility in their work hours. Can this continue if some or all of them become non-exempt?

Yes. Flex scheduling is allowed within the same work week. As an example, let’s say a typical schedule is 8 hours a day during the day, and the department needs an employee to work a special event for 4 hours during the evening. The schedule may be changed to give the employee 4 hours of time off at another time during the same work week.