Can you add a clip of a song to a movie on Windows Movie Maker?

Yes, but its not easy.

In order to be able to use a video clip in movie maker, you will need to have it saved on disk as an avi, mpeg, wmv, asf or any other video format supported by movie maker. There are a few firefox plugins made specifically for saving YouTube videos to disk, but the legality of doing so is questionable. Additionally, YouTube goes out of its way to limit the functionality of these plugins & thus restrict you from saving the videos to disk.

I have had very limited success with these plugins.

The best option is to contact the person who posted the video and ask if its okay for you to use it in this way, and if so, if they wouldn't mind sending you the video in its original format.