Of course, the letter come first chronologically, but all it did was to clear away some of the underbrush, so to speak. After reading it, Lizzy no longer believed Darcy to be dishonorable, but she still could not approve of him. Even when she is being shown around at Pemberley, we are told that, "That [Darcy] was not a good-tempered man had been her firmest opinion."

All the letter did was convince Lizzy that Darcy was not dishonorable. Therefore, it cannot, IMHO, be said to have "done the trick." It opened Lizzy up to later thinking better of Darcy, when presented with the evidence of his character through his home (as Mary Ellen explained so nicely) and the testimony of an intelligent servant, it was not the letter that convinced her, beyond convincing her that Darcy was not dishonorable.