Not really, it's a bit swift for a sad song - and her voice doesn't do it for me.
Has anyone heard of Johnny Ray? He was a 1950s singer who was given to singing self-indulgent, weepy-type songs, one of which was called Cry.
It was a terrible song, but apparently he used to sob most of the way through it and the audience of (mainly) women would sob and howl! he was a huge heartthrob but to see him you would think he could anyone excited.