Are you only planning the one park day, or are you getting a ticket for the other days? If the latter, depending on the length of your main ticket you may be better off adding a day to that for $5 (as of August 5th, the incremental cost for days 5-10 is now $5). Then you can use the GAD voucher for something else like the FP Exchange Card (although no guarantee you can use that during EMH) or the souvenir ear figurine.
EMH is an on-site guest feature, although you still need to have paid admission. Doesn't matter the source of the ticket, as long as you have your KTTW card (your room key) to get in to the park (if entering after EMH starts) and to get on attractions.