The ceiling fan in my bird room runs 24/7 during the summer with no problems. I even built a cage around it so I could run it while the birds were out.
Birds aren't as sensitive to drafts as some people will tell you. They have to live with the wind in the wild and can deal with it. Constant cold air blowing on your bird isn't a good thing, so don't keep your bird right in front of the air conditioner. But air that's simply moving without being particularly cold isn't a problem.
I don't remember how I managed to survive before I built this lol.