This is a great question! It seems to me that the song that Jose sings actually foreshadows the events that occur later in the story, in particular the death of Mr. Scott and the confrontation that Laura has with his dead body, and the resulting epiphany that she experiences. Let us note the lyrics of this song:
This life is Weary,
A Tear--a Sigh.
A Love that Changes,
This Life is Weary,
A Tear--A Sigh.
A Love that Changes,
And then... Goodbye!
Clearly the song comments upon the general weariness of life, followed by the final exit of death. Note, too, that Jose's manner of presenting this song likewise mirrors her reaction to the death of Mr. Scott. Although she starts by looking "mournfully and enigmatically" at Laura and her mother, after the end of the song, "her face broke into a brilliant, dreadfully unsympathetic smile."
However, this song foreshadows Laura's meeting with the corpse of Mr. Scott. Note what she thinks as she looks at him:
He was dreaming. Never wake him up again. His head was sunk in the pillow, his eyes were closed; they were blind under the closed eyelids. He was given up to his dream. What did garden-parties and baskets and lace frocks matter to him? He was far from all those things. He was wonderful, beautiful.
It seems that Laura experiences something of an epiphany as she regards the peacefulness of Mr. Scott's body. After focussing so much time and effort on the frivolous concerns of the garden party and "lace frocks," she is struck by his tranquillity. After the "weariness" of his life, and his "goodbye," as the lyrics of the song suggest, he has found a peaceful release that makes him "wonderful, beautiful," which in turn makes Laura realise the "weariness" of her own life.
Thus the lyrics of the song that Jose sings seem to operate on a number of levels. It foreshadows the epiphany that Laura has towards the end of the story whilst regarding the body of Mr. Scott, and it also indicates something about Jose's character and the unsympathetic way in which she will greet the news of Mr. Scott's death. Finally, it acts as a comment on the social drama of the garden party and its meaninglessness in the big scheme of things.