I'd question whether there's any significant difference between the extent of that kind of cheating between faith schools and others. To the extent that any school, or any type of school, has a reputation as a good school, parents are more likely to try to get their children to be admitted, and that can mean a sort of positive feedback.

One noticeable thing with our local Catholic comprehensive is that it has a noticeably higher proportiont of children from African and Asian families, many of them non-Catholic or non-Christian. I had a Muslim friend who sent her children there, and she was asked to supply a note from the Iman to confirm their religious status.