Lots of crazy things go down in The Scarlet Letter—like eyes that glow red; meteors in the shape of an "A;" and witches who hang out with the Black Man in the woods. But this is more fable or fairy tale than horror movie. We're not so much concerned with whether these supernatural occurrences are real or not, as we are with what they're telling us about our characters—and the secrets they keep.
In the world of The Scarlet Letter, the supernatural is anything that cannot be explained.
Pearl's eerie intelligence and elfish ways are just a product of being excluded from society. The girl's got no social skills.