Can "The Rocking Horse Winner" be considered an allegory and/or a fantasy?
This is a great question because it points towards the fantasy nature of this story. However, you need to remember, allegories are stories where events, characters and actions all stand for something beyond themselves. Normally characters and setting will represent abstract ideas or moral qualities. Whilst it appears the story is almost fable-like in pointing towards the dangers of greed and its impact on not just yourself but those nearest and dearest to you, it is clear that we can not view this story as an allegory.
However, it is clear that Lawrence uses many of the conventions of fantasy in this excellent short story. Consider the many fantasy elements--the repeated whispering of the house, the possession (if that is what is is) of Paul by the rocking-horse, the way that with more and more success Paul becomes more and more deranged. It is clear by contrast that a typical fairy tale ends happily, but here Paul dies and his mother is left with the consequences of her greed. We can thus say that Lawrence adopts the trappings of the fantasy only to subvert them to his own purpose - the shock ending stresses Lawrence's point about the evils of materialism.
So, this story cannot be considered as an allegory, but you are right in identifying that Lawrence deliberately adopts the genre of the fairy tale - but only so that he can subvert it to emphasise his message and theme.