You could write a bash script to move the file from the download folder to the music library too.

Haven't done any bash scripting in a minute so sorry if this is off, but you get the gist:

For files in /path/downloads/*; do mv "$files" /path/musiclibrary/; done

You can also output a list of all the files in your music library with ls -alR /path/musiclibrary >> /downlaods/musiclibrary if you want a list

Which you can grep for a file name to check if it's there