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There is such a thing as corrective rape that is practiced in parts of Africa, India, and Thailand. However, it is generally rooted in cultural ideas of heteronormativity and is most often used as a form of retribution or punishment for perceived lewdness rather than any specific curative religious ideology. While anything is possible in the world of fringe cults, I have never heard nor could I find any evidence of any Christian sect or cult that practices it as a tenet of their faith.
A quick Google search of the phrase "curative intercourse" just leads to a few pages of links referring to that episode of SVU before veering off-topic. It looks like the writers of SVU coined the phrase themselves.