I think it's going to be split. People will study them, but it will be the same as they do nowadays. Mozart wrote a lot of music, hundreds of pieces, operas, operettas, piano solos, whole orchestra instrumentals. Basically, he had a masisve back catalogue, of which most people know Fur Elise.
Music buffs know more songs, but most people recognise the tune, but may not even know it was Mozart. This is probably the fate of rock musicians, people may still know the name Hendirx in 200 years, and they may also recognise the opening notes of Voodoo Chile, but they won't connect the two, and only dedicated music students will have any idea of other songs.
But at least that's better than current pop music (2000-2010), which in the future will be remembered as 'That generic period characterised most by synthesised drum beats and a absolute lack of talent and notability.'