No extra steps are required in regards to Integration linking or synchronization. The students will remain linked to The Education Edge once they are converted to Constituents in The Raiser's Edge.

You may consider whether or not you want to stop sharing the graduates' addresses with their relationships' addresses all the time or only one by one as address changes are received from the graduates. This consideration should be made because if the graduates' addresses are currently shared, edits to their existing addresses in the future will affect the shared parent/sibling addresses.

For more information on Integration, refer to:
How to stop sharing addresses in Raisers Edge and Education Edge after student graduates (BB708950) 
What is Integration? (BB220850)