Actually, it only saves datablocks in Your cache.db. The rest of add-on code is executed server-side. (unless it's client add-on, then either You just get a message "Hey! Click here and download this awsum gui for server!" or You download the client add-on from somewhere, like Add-Ons section)
/topic
There is no "native" way to download those datablocks, though there was some way to download them, using Mission Editor if I recall correctly. Music is datablock, so if the server is still online, You can either talk to the host ("Hey man, givmeyamusicpl0x!!11!!!!1!111111") or
download Mission Editor Add-On and experiment with it until You find a way.
If the server isn't up anymore and You're desperate to get that music, You can try to decrypt cache.db, but it's really difficult.