Yes, they can! Seesaw supports a unified student journal across classes, grade levels or school years with Seesaw for Schools.
In the free and Plus versions of Seesaw, it's not possible to keep journals intact when you move a student to a new class or year. Moving students from class to class (or year to year) is only possible with our paid school-wide service.
For teachers using the free or plus version of Seesaw, we recommend that the new teacher start fresh by adding students as new students in the new class or new year.