Does wearing a mask when you are ill actually protect anyone else?

Yes, and this is the direction where masks work best. A surgical mask on someone who is coughing substantially reduces the droplets they put into shared air — this is called source control and it is well supported. Protecting yourself from others is harder and needs a well-fitting N95 or KN95 rather than a loose surgical mask. Practically: if you are ill and cannot avoid a crowded bus, office or clinic, a mask is one of the more considerate things you can do. Fit matters more than material — gaps at the nose undo most of the benefit.