The unnamed narrator is a member of the town where Emily and Homer die. The reason Faulkner chooses to go back in time rather than from the time of the funeral is because the narrator, and by extension, the town, are figuring out what exactly has happened to bring about this tragedy.
The answers he finds are uncomfortable. Faulkner often uses the pronouns "we" and "our" to demonstrate the culpability of everyone who ignored and isolated Emily.
As the narrator gradually becomes aware of her mistreatment by neglect, so too do we as readers. It helps establish just how and why Emily went off the deep end. Still, it is quite a shock, not only to find Homer's corpse and discover Emily's death, but also to understand that she was so incredibly lonesome that she slept by his body all that time.
The force of the shock, I think, helps wake up the characters. For me, and a host of other critics and readers, the story would not be nearly as compelling if we did not understand the motivations of Emily and the neglect of the town before the discovery.