I don't know how radio stations handle "Alice's Restaurant" since I listen to my own copy but I did see Arlo Guthrie sing it live at a concert when he was in town a few years back. When the song got near the slur, he stopped playing for bit and went off on a short tangent before picking the song up after the slur. It's his song so I doubt anyone minded him changing how he performs it. The change felt a lot more natural than simply bleeping or cutting the audio.