The name of the narrator's first cat, Pluto, is also the name of the Roman god associated with death; he is the equivalent of the Greek god, Hades, the Lord of the Underworld. Pluto is, then, heavily associated with darkness and death. Although the narrator initially has a wonderful and loving relationship with his cat, Pluto, that relationship degenerates as the narrator becomes an alcoholic (succumbing to "the Fiend Intemperance," he calls it) and turns violent and cruel. One night, when the narrator comes home drunk, he antagonizes the cat, who bites him, and he responds by cutting out the cat's eye. The narrator becomes more and more "perverse" in spirit, eventually murdering the cat by hanging it by the neck.
The narrator's abuse of Pluto begins a chain of events that leads to his own demise (after murdering his wife). In this way, Pluto seems connected to death and darkness, in part because of its color, but also because the cat's existence launches the narrator on a path consisting of death and darkness. The narrator's own disease, alcoholism, changes him, turning his soul black with sin. Though the cat itself is not evil, he seems to symbolize the influence of evil that impacts the narrator and turns him into a monster.
Your idea is plausible, but I think Poe was thinking of a different Pluto when he imagined this story of a man terrified of a cat. Pluto is the name of the Roman god of the underworld and the judge of the dead, whom the Greeks called Hades. The color black is also associated with Pluto; black sheep were given to him in sacrificial offerings.
In both Roman and Greek religious beliefs, unless a person received a proper burial, his or her shade was doomed to wander the earth, haunting the one who had done them harm or had not given them the right kind of funeral. Although what haunts the narrator is a cat, I think we can apply those beliefs to the cat's haunting the man as well. Is the cat really a spirit that is haunting him? Or is it his guilty conscience? That's the subject of another question!