Anon-kun brings us some excellent worldbuilding material.

Hey, you want to hear something?

If there are souls, and they aren’t just glorified backup devices, but are involved in our decision-making process, then the behavior of an ensouled body must be different in some way from an unensouled body.

And thus, the behavior of ensouled matter, too, must be different from unensouled matter.

The degree of difference in behavior from the hypothetical unensouled version would determine the magnitude of interference.  If it’s fairly high (and it would need to be in order to justify certain religious beliefs), then it should be detectable statistically by comparison with control atoms.