Yes they may ride Magical Express.
The CM will have to make the DME reservations since his name heads up the room reservation. This is similar to the situation where you rent Disney Vacation Club points and the club member, who sets up the room reservation, has to make the DME reservation.
Closer to check in day (something like 3 days out) "ownership" or "control" of the reservation passes to the check in desk and the guests may call the DME hotline to make the DME ressie if that was not already made. Guests have had limited success jumping the gun and calling DME sooner.
Magical Express hot line number: toll free 866-599-0951