No, a teacher does not have access to make changes to student designs.
There are some possible workarounds for this:
The teacher could log into the student's account and edit the design.
The student could make their design available for others to copy and the teacher can edit a copy of the student design in their own account. See instructions below:
As the student, make the design available to copy:
If you ensure the Price of the design is 0 and the Privacy is set to Show, then this will allow the teacher to copy the student design and make changes in their own account
Now, once logged in as the teacher, they can find the design and click the gold token to copy the design: