A version of one his songs, "I Shall Not Walk Alone", by The Blind Boys Of Alabama was in the episode "Confidence Man". That was the episode about Sawyer, and the people he tried to con. But the song was actually played at the end of the show. A fantastic TV moment.
I don't think there's ever been a Ben Harper-sung song in the show. They've used Damien Rice, Joe Purdy, Willie Nelson, Patsy Cline and the aforementioned Blind Boys. They do pick some great songs for this show.
About "I Shall Not Walk Alone" - Ben Harper released it on one of his albums (I'm not really a fan, so I don't know which one) and he later produced the album "Higher Ground" by The Blind Boys. The song is on that album, and it's incredible (one of many on the album - Tom Waits and Prince covers as well).
Hope this helps a little.