Yes, they will. However, honestly, it's just easiest to tell Disney Reservations that you all need DME, but don't know your flight numbers yet. (They will just mess it up. The reservation owner will receive all of your tags and DME tickets and will need to distribute them to the individual folks.
Then once your tags arrive, call the direct DME number and give them your specific flight numbers and they will get it correct in the computer. Then when you arrive at the DME desk, confirm that they have your departing flight numbers correct.
The arrival times are really only for planning purposes for personnel and buses. Your departing flight time is the critical one as they schedule pickup times at your resort based on flight times.