Edgar Allen Poe loves to use dashes in his work. He uses them frequently in "The Black Cat," along with other works such as "The Pit and the Pendulum" and "The Tell-Tale Heart." Indeed, these dashes do help us hear the fragmentation of his thoughts, as your question mentions. They also show a crazed feeling or emotion. His mind seems to be bouncing around from thought to thought, almost faster than he can pen the words.
This style of writing serves to evoke suspense in the reader. It is a very "gasping" form of conversation, and this causes tension to build in the story. Because the dashes link several thoughts together rather than end each thought, information is piled on the reader in a rather stressful way.
Take, for example, this excerpt from "The Black Cat":
"The reader will remember that this mark, although large, had been originally very indefinite; but, by slow degrees -- degrees nearly imperceptible, and which for a long time my Reason struggled to reject as fanciful -- it had, at length, assumed a rigorous distinctness of outline. It was now the representation of an object that I shudder to name -- and for this, above all, I loathed, and dreaded, and would have rid myself of the monster had I dared -- it was now, I say, the image of a hideous -- of a ghastly thing -- of the GALLOWS ! -- oh, mournful and terrible engine of Horror and of Crime -- of Agony and of Death!"
The dashes in this selection serve to insert a gasping feeling between each thought. It helps the reader to feel the madness and panic that the character is experiencing. If Poe had chosen to simply use commas or periods, then the sentences would seem more commonplace. But because the usage of dashes is meant to add emphasis, frequent usage will serve to emphasize strong feeling in a passage.
Poe's use of dashes in this way ends up being extremely effective, and many of his works are well known for the heart stopping terror they give to their readers.