Some of this is a real stretch. Alice Cooper didn’t see real fame under Zappa’s tutelage. It was only after the band moved to Detroit they hit the big time (used to go to their early shows in Michigan). They recorded “Love It to Death” in a barn in the Detroit area and re-mixed it in Chicago. The title song never made it on an album, and I haven’t found it on anything other than a 45 RPM. I used to have it.
Cooper has never attributed his act to anything other than theatrics. He was not a follower of the occult and laughs this off whenever he sees it.