Bellyman Frank Sinatra? Raspy tone? Both Frank and Dean Martin smoked, and like you said, often had a lit gasper while performing. Two of the smoothest crooners ever. Judy Garland and Sarah Vaughn smoked.
I once went to a Dionne Warwick concert, had a great seat, could see her offstage taking the final drags before coming out. John Lennon and Paul McCartney smoked, as did Crosby, Stills and Nash. Joni Mitchell smoked. Not a raspy voice in the bunch.
On the other hand, Tom Waits, Dr. John, Joe Cocker and Janis Joplin were smokers. Jimi Hendrix and David Bowie smoked, too. Probably more to do with genetics than tobacco. And, no, I never smoked, other than the odd Newport the drummer in a band I played in during high school would offer.