Yes, you can tie this amazing story to Trancendentalism. According to Holman and Harmon, the transcendentalists "agreed that within the nature of human beings there was something that transcended human experience--an intuitive and personal revelation." They believed in living close to nature, believed in the individual, and emphasized spiritual connections and living.
Usher is absolutely "connected"--to his sister, to the house, to the narrator. His connections to his sister and the house bring about the destruction of all three, since one can not become ill and separate from the other two. The spiritual connection or supernatural connection bonding them together also takes them all down in the end.
The narrator often speaks of how isolated and dreary the house is on the inside. They are isolated from nature...something the transcendentalists admired and loved. This is part of the reason (readers are led to believe) that the house and its inhabitants suffer. All is better when one is close to nature, and through nature, close to God.
Lets first define. Romanticism focused on the imagination, human spirit, an idealization of nature, and emotional freedom. Transcendentalism was characterized by a belief that emotion, as opposed to reason and logic, could help transcend the human beyond a merely physical existence; it also emphasized the belief that humanity was essentially good. Dark Romanticism grew out of both movements and showed the style of Romanticism with the spiritual expression of transcendentalism, but showed a strong belief that man was flawed by faulth and sin.
"Fall of the House of Usher" represents Dark Romanticism at its core. It has the symbolicm representation of nature in the description of the house and the storm. The natural elements are intertwined with the narrator, who has "sympathetic vibrations". He is so in tune with humanity and nature that he withdraws himself from both, claiming to suffer from "nervous exhaustion." He gets beyond these instinctual reactions, however, choosing to try to explain them through intellectual pursuits. Contrarily, however, he refuses to allow science to examine the condition and "death" of his sister, believing that science is flawed. In truth, however, it is both he and his sister who are flawed, who suffer from insanity that is the result of intermarriage. The story is related to trancendentalism in the fact that trancendentalism has influenced dark romanticism.