Can't access Supersearch at present to verify. However, there is a variant of I'm a Rover, and Seldom Sober sung by Davie Stewart where Molly turns up (alive and unaccompanied by swans!).The chorus goes:

I'm often drunk, and seldom sober
I'm a constant rover from town to town
And when I'm dead and my days are over,
O, lay me down, my Molly Bann.

I'm not sure her life in this song is much to be envied; her lover is an alcoholic rambler, who tends to turn up late at night, when she is trying to sleep. He demands to be let in as he is exhausted and soaked to the skin!
The song is on Davie Stewart Topic 12T293, reissued on CD by Greentrax as CDTRAX 9052. There is a similar song by John (Jacko) Reilly but its not currently available.