In the short story "A Rose For Emily," does the fact that Emily is a woman factor into the lonely aspect?

In my opinion, the fact that Miss Emily is a female is a major factor in her loneliness. This is because of the nature of the society in which she has been raised.  She has been raised to be a Southern belle, by a dominating father.  This means that her father was expected to approve or disapprove any suitors, choose with whom she could associate, and see to it that she was educated in a way that promoted her loneliness.

A male raised in this time and place would be more likely to choose his own mate. But Miss Emily's father disapproved of all the suitors who presented themselves, thus assuring that Miss Emily did not marry beneath her, but stayed at home instead, caring for her father, and living a lonely life.

Because the Grierson family was the wealthiest in town, the ruling class, really, Miss Emily was raised to avoid any association with the townspeople, who were not up to par socially.  A male would have had the freedom to associate with anyone, perhaps not inviting townspeople to dinner, but certainly having the wherewithal to come and go and befriend others outside the house. Males were accorded a great deal more latitude than females in setting.

We can infer that Miss Emily's education prepared her only to be a suitable wife for a wealthy man. It did not prepare her to get a job, which would have allowed her a whole new world of relationships.  A male would have been educated for employment, I would say, so he would have worked at something and been far less lonely.

This story could never have realistically played out the way it did if Emily had been a son instead of a daughter. It was only Miss Emily, the Southern belle, who could have been subjected to these conditions, conditions that caused her a lonely life and a lonely death.