The Meaning of Life, the Universe, and Everything.
I do not believe there is any way to add the sound to the server itself. Your best bet would be to change the music of one of the records to the sound you want in a resource pack and put it at the server's pack with a prompt to download. As long as people are running your pack you could play the record with your song using a commandblock to target everyone, it's just that anyone without the pack would hear the default MC record.
i tested this out, and all seems to work except for one problem. we are already using the Faithful resource pack already prompted by the server. i went in and changed one of the discs in the faithful pack to play the sound and tested the /playsound command it all works.
the only thing now is where/how can i upload this modified version of the faithful resource pack just solely for our server to prompt it, and to obviously not distribute it anywhere.