The Wii Photo Channel cannot play or download music—it's strictly for photos. To listen to music on Wii, use the built-in Music Player with external storage.
Wii Music (2008) lets you play instruments, arrange songs, and download additional tracks via Wii Shop Channel (now discontinued; only pre-purchased content works).
The Photo Channel's "Music" feature is simply a playback interface for files on USB/SD—it does not download or store music itself.