Not in my view - if there are no words or vocal melody, it's not a song, it's just music.Song's can be instrumental too.
So Johnny never wrote or gave songs to Morrissey. He composed, usually, basic backing tracks with some rudimentary guitar melodies , sometimes I think the band composed the backing track together, with Andy's bass line being the key melody at that stage, then Marr gave them to Morrissey who then recorded his vocal melodies/words. That's when the song was created. So the songs were Morrissey's, the music was Marr's, or Marr/Rourke, or sometimes Marr/Rourke/John Porter. Take away the backing music again, and you'd still have the song (the vocal melody and words). Once the song had been created, it was then usually beefed up in studio - now that the vocal melody was in place, layers of guitar harmonies could be added.