Adding Documents to Media Library

When adding a document into the Media Library, does the document have to be located in OneDrive?

Are you referring to the Presenter Media Library? Files are imported from the computer. Documents (.word, .pdf, .excel, etc.) are not supported file types.

Anything that you add to the media library is copied to a central repository managed by Worship Tools. It does not matter where the file was stored before you copied it.
The lyrics of songs are also stored centrally in the lyric library.
This then makes it all available to any other computer logged on with an id linked to your Church's account.
Once you have added it to the media library, you can delete the local copy if you want.