Yes, Delta Elites (Silver, Gold, Plat, Diamond) are also exempt from the fees, just make sure your name and sky miles number are linked to the reservation.
Link to that specific rule here:
https://pro.delta.com/content/agency...ction-q-a.html
For the full list of benefits as a Medalion Member see this:
https://www.delta.com/content/www/en...-benefits.html