As long as you have park hoppers you can go over to the Studios (or any park with the EMH evening hours) and participate. Of course, you also have to be a Disney resort guest. You do not have to be in the evening EMH parks before closing to get your wristbands and participate in the extra hours. You can get there anytime and show your resort ID and they will admit you and give you a wristband.
In case you did not know, you can exit Epcot at the International Gateway and either boat or walk to the Studios. The boat takes around 30 minutes but the walk is always faster unless you catch the Friendship boat immediately.