How would the story be different if it had been a picture of a white Virgin Mary?
Your question is pertaining to the symbolism of The Black Mary.
The Black Mary is symbolic and extremely important to many of the main characters. First, it is important to Lily because a picture of it is one of the few items that Lily has of her deceased mother. Had this Mary been depicted as White, then it was not be so distinguishable; Lily would not have been able to use the image as a guiding tool to find her way to the Boadhouse's home.This image is also important to Lily because the Mary is the "ideal" mother, and what Lily is seeking is information about the mystery behind her mother's life.
The Black Mary is also a symbol of motherhood and the empowerment of women. August Boadhouse, when placed into the context of her being a single, black, woman in the Jim Crow south, is the epitome of power and grace. The Black Mary is an idol of worship to the Boadhouse sisters, and especially August, because The Black Mary represents what these women are -- they break from the stereotypes that surround black women; they are expected to be ignorant and dependent, but August, June, (and even May), are independent, powerful, and very intelligent. The Black Mary breaks from the stereotype -- the Virgin is also expected to be White, but this depiction of her is just as graceful and maintaining the same affect.