No definitive answer exists to this question as it has not been extensively studied. However, there are some potential risks that could make a baby sick if they are exposed to fan air. For example, if the fan is blowing directly on the baby or if the blades are covered in dust, these could both cause respiratory irritation. Additionally, if the room is very cold, the baby could develop hypothermia. Therefore, it is best to use caution when using a fan around a baby and consult with a doctor if you have any concerns.