The welcome center will stay open until all guests scheduled on flights have arrived. So even if your late night flight is delayed and they have your flight information on record someone will be there to greet you and board you on a bus.
Just make sure they have your flight information in their system, pack a carryon with what you need to go to bed and get up the next morning, and tell bell services to hold your luggage for the next day. Your luggage will be delivered while you are at the parks the next day.