No, it does not. I am guessing that at some point in the distant past of the resort these rooms perhaps did not have A/C, but now all rooms have A/C. The screened windows have wooden shutters that you can adjust to permit air and light or close as you prefer. The rooms will be as cool as you care to make them or as open and "natural" as you like. I believe all rooms also have ceiling fans to help keep things comfortable.
There is AC and it works really well. We throw open the shutters in the day and run the AC at night. We like the BFS's at CSA and the fact the have screens and shutters. Turn down service will close everything up a night while you are out to dinner or entertainment.