DISer posters have said that the monorail does operate for EE with the first monorail arriving about the same time the first guests enter at the main entry. That's the way it used to work when EE was offered a few years back. I suggest you check with the hotel when you check in, because it is subject to change. If you cannot confirm that the monorail will be operating for EE, I suggest you walk down to the main entrance to be on the safe side.
Remember also that EE is always subject to change. While these unofficial sites will tell you that EE is typically offered on Mon, Tue, Thur, and Sat, dats are always subject to change (although, I've only been aware of changes for June Grad Nights or other special parties). To be on the safe side, check with your hotel when you check in to confirm the schedule for EE. Good neighbor hotels should have this info as well as the Disney hotels.