Yes, we can hear beauty. The melodious sounds of birds chirping during the dawn and dusk.
The lines: "Heard melodies are sweet, but those unheard are sweeter" are taken from a poem named "Ode on a Grecian urn" and is written by John Keats. This means that whatever we hear (which is already created) is definitely sweet but the one which comes from within and is never heard before is much more sweet and soothing.
Yes, I have heard a few such songs in my head long after the song was played.