Does the Scheduler need to be run before running Copy Students into Summer Schools? 

It is NOT necessary to run the Scheduler before copying students into the Summer Schools.  It can be run before or after.  However, the yellow message below is a Reminder Notification that if using Scheduling Terms the Scheduler does need to be run before copying students into the Summer School in order to map the Summer School Term and the actual term

The Scheduling Term drop-down can be used as a map between the Summer School Term and the actual term in the Term (TRM) table.