The "unnatural death" (are syphilis and violence "unnatural"?) is only implicit if the song is considered within the context of an academic study of its "song family". Looking at SJI on its own, there is no suggestion whatever of syphilis or violence within it. The gal could have died of TB or in a car accident - it is really immaterial. If they felt the cause important, the singers who passed down and/or altered SJI would have included at least some hint of it - I don't think they would have assumed their audiences were familiar enough with The Unfortunate Rake tradition as to take the song as a warning of the dangers of bad girls and the pox.

I don't think the references to bars, gambling, and chorus girls have to suggest violence and disease, either. They could just suggest good times.