In most versions this is the general theme of the song so you are correct. In some developments dating back to the 18th century she has already hung herself and the introductory verses are her suicide note, but in actuality this episode was introduced from an Irish broadside called 'The Rambling Boy' of the late 18th century. It appears most noticeably in the American oecotype 'The Butcher's Boy', but also appears in some later English versions probably brought back over here by American forces in the 2 world wars.