Hi Amanda:
You've touced on two important points: one is that of role modeling and the other is efficient time management.
When an unprepared teacher conducts class, it's gonna take more time and the lesson will be less complete. The students will probably notice the disorganization and not appreciate it.
The other is role modeling. When student come to class and are greeted by name by the teacher, and there is time to visit casually or perhaps answer a student question. That stands out. When the lesson begins, the topics are presented in an orderly, calm, and relaxed manner with topics smoothly transitioned from one to the next. Again students will noticed.
Organized teachers can demonstrate through daily practice the techniques and benefits of organization and being prepared.
Regards, Barry