Yes, you are right, he will be a Jew turned counterfeit Christian, just as Jesus was a Jew.
Certainly Satan mimics God...but at what point does the exact mimicry cease. Is the AC born of a virgin, is the virgin a Jewess, is she a direct descendant of David?
Without some scriptural reference or some logical/formulaic extraction thereof...your suggestion is nothing but suggestion.
This matter (to believers) is too darned important to be compounded by hearsay and feelings.