Ofcourse not. Record-labels do not post music on Spotify. Spotify takes action and asks and pays record labels to get music available. And they do that quite good as a lot of music is available. I want to help them doing it even better, by asking for these specific missing songs.
The record label or the company/person responsible for the rights of Elvis Presley and Bach songs probably approached Spotify. And yes they do have a department that handles Spotify for Artists applications and requests. Both big, small and up-coming creators approach Spotify because Spotify is one of the best ways to get your music heard.