Unfortunately, this is not something that is possible with Spotify. In order for Spotify to play any local files that have been synced in its library, it must be able to pull the file from your hard drive. Otherwise, you will have the track names on Spotify but will be unable to play them.
Spotify has millions of songs! You can try searching through the catalog to replace some of the tracks from your backup disk with tracks from the Spotify catalog.
Hope this helps!