Q. How Can I notify students that a File has been uploaded to the Files area?

Yes and No.

1) The first thing that has to happen is the "Files" tab must be enabled on the left hand navigation. 

2) The second thing that has to happen is that students must change their notification settings to receive File notifications. By default that notification is turned off.

Both items 1 and 2 must be true in order for students to receive notifications about files being added to the course.