There certainly are birds. Seen them on numerous occassions. Remember that there is powerful HVAC equipment which keeps the air pressure inside the building higher than the outside. Thus, smaller creatures, such as bugs, would have to fight that perpetual wind to get inside. Crawling ones might have an easier time, but Disney likely has significant amounts of pesticides to ward them off. Plus, bugs tend to keep to the ground, rather than scaling concrete unless they have a food source or have run out of food/shelter below.
And as we all know, Chef Mickey's can hardly be considered a source of food! No, just kidding, had a great time there the morning of my wedding with my best man and brother-in-law. Saw birds, no bugs.
-Andrew