Nah, I don't think the motorcycle accident had anything to do with his voice. I read somewhere that he quit smoking around the time of "Lay, Lady, Lay", but I don't know if that's true either.
/By the way, he was supposed to do the soundtrack for the 1969 movie
Midnight Cowboy, but he bailed out. "Lay, Lady, Lay" was intended for that project, and probably would have been the title song.
As it happened, the title song was Harry Nilsson's "Everybody's Talkin' At Me".
Midnight Cowboy-Everybody is talking at me(Full Song)