This is an opinion-based question, so you can feel free to answer the question either way. The important part will be to support your opinion with evidence from the text.
I do believe that Emily kills Homer. I believe that two pieces of evidence strongly support the conclusion that Emily kills Homer. Since the story isn't told in chronological order, the two pieces of evidence are given to readers in reverse order. In section three of the story, readers are told that Emily buys arsenic. She goes to the druggist in order to buy some poison, and she says that she wants the strongest one that he has.
"I want the best you have. I don't care what kind."
The druggist named several. "They'll kill anything up to an elephant. But what you want is--"
"Arsenic," Miss Emily said. "Is that a good one?"
"Is . . . arsenic? Yes, ma'am. But what you want--"
"I want arsenic."
Notice how the druggist attempts to inform Emily that she doesn't need to spend money on the most potent poison that he has. He tries twice to tell her what she wants. The druggist is probably assuming that she has a rodent problem of some kind; therefore, she would have no use for something as potent as arsenic. She has no need to kill an elephant; however, Emily is certain that she needs arsenic. The druggist is legally required to ask her what her purpose is for needing arsenic.
"Why, of course," the druggist said. "If that's what you want. But the law requires you to tell what you are going to use it for."
Emily's response is quite foreboding. She doesn't say anything. She simply stares down the man until he looks away and retrieves the arsenic. She could have lied and said it was for rats, but her evil stare sends readers a sinister message. She must need something strong enough to kill something big.
Shortly after purchasing the arsenic, readers are told that Homer is never seen again. Perhaps he left town. That's what I initially thought when I read this story for the first time. But now I know better. Faulkner drops an important piece of information about Homer going missing in section two of the story. In that section, readers are told that the strong smell appears shortly after Homer disappears.
So SHE vanquished them, horse and foot, just as she had vanquished their fathers thirty years before about the smell.
That was two years after her father's death and a short time after her sweetheart -- the one we believed would marry her -- had deserted her.
By putting together those two pieces of evidence, I feel that it's safe to say that Emily kills Homer. She buys a poison strong enough to kill an elephant, shortly after Homer is never seen again, and shortly after that a strange smell develops.