Does the alternator make a noise when charging the battery?

An alternator has fast moving parts surrounded by air, so it will make a noise in operation, in much the same way a desk fan makes a noise. (The fan blades spinning in air.)

Under heavy load (battery fully flat) this noise often becomes very slightly louder, due to increased tension in the drive belt causing increased loading on the bearings and the belt, but it would not normally be enough to notice unless tryingto notice it.

If the noise is very noticeable it is probably because one of the items the belt runs on has a bearing in the early stages of failure.