Certainly Akakyi's demeanor is affected by the overcoat, considering the sacrifices that he had to go through in order to place upon his shoulders a beautiful and well-made piece of clothing that also represents Akakyi's one and only indulgence in life.
The overcoat definitely rubbed on Akakyi's ego and personality. As the story progresses the reader may even conclude that they have, indeed, become one, or at least dependent on one another. Either way, there is no doubt as to the power of the overcoat in Akakyi's mental state. The narrator tells of how Akakyi was on a "holiday" mood, feeling cheerful and always mindful of his coat.
However, we must remember that Akakyi's character (while he is alive, that is) is not meant to be dynamic: it is precisely the rut of Akakyi's life what brings him out as fun and interesting. It is also his weird personality that sets him aside from the rest of the men. This is why it comes to no surprise that he is still shy and reserved at first with his co-workers.
It all changed afterwards. When a party was proposed to "baptize" the new cloak, Akakyi's happiness knew no limits. The problem was that, as he reached it, he was still feeling odd, obsessive about the little things, and out of place.
He simply did not know where he stood, or where to put his hands, his feet, and his whole body. Finally he sat down by the players, looked at the cards, gazed at the face of one and another, and after a while began to gape, and to feel that it was wearisome, the more so as the hour was already long past when he usually went to bed.
After that, it all goes downhill; he gets assaulted on the way home, his overcoat is stole, and the system completely fails him. After his death, Akakyi still aimed to seek revenge and justice from beyond, achieving it shortly after. Therefore, his character never undergoes a change that would redeem him in the eyes of his co-workers. Akakyi is meant to be a strange and unique man.