The op asked if ELVIS sang any folk songs, not whether half of his repertoire have become folk songs because they are sung by ordinary folks for their own pleasure,
ordinary folks sing opera for their own pleasure and play classical music for their own pleasure, ordinary folks play jazz for their own pleasure, in fact most forms of music are played by ordinary folk for their own pleasure but it does not make them folk songs
I used to play pop music from the sixties. during the early sixties, but it was not folk music. it was the hits of the day, that i was playing for my own pleasure all of us in our group knew what it was and it was not called folk music by any of us.
when i saw jimi hendrix it was jimI hendrix not bloody folk musiC FFS