An interesting question. My first thought was no, that the narrator was male, because of the authority with which he/she speaks and the period in which this was set, but also because the narrator distances him/her self from women, saying, for example, "The two female cousins came at once." It is hard to imagine a woman referrring to other women as "female." However, upon reflection, I'd say the narrator distances him/herself from men as well, writing, for example, "Already we knew that there was one room in that region above stairs which no one had seen in forty years, and which would have to be forced. They waited until Miss Emily was decently in the ground before they opened it."
In this period, men would have been the ones opening the door, so this seems to distance the narrator from men as well. I'd say this is an intentionally sexless narrator, like a disembodied spirit, but that it sounds a bit more male.
I don't believe anyone could prove that the narrator is female, although certainly the voice is that of a gossip. However, a small southern town of this period (early 20thC) would have male gossips as well as female. In addition, the narrator frequently refers to "the ladies" as doing this or saying that, but uses "we" in reference to the town as a whole. The last few paragraphs are interesting in this regard. In part V, the narrator first refers to the "female cousins" who arrived after Emily's death (which would be strange for a woman to say), then refers to the "town" visiting at the funeral, here mentioning both "ladies" and "gentlemen." The narrator then moves to "we" to explain finding the hair on the pillow ("For a while we just stood there...)". While perhaps one could make an argument that no male narrator would show the compassion that this narrator shows for a woman's plight, I nevertheless cannot find textual evidence to support that.