Spidey Sense Crowley is a demon and she is 100% OK to sense something unnatural is up with him. She's dealt with demons before so you can make of it whatever you'd like.

Demonic Crowley is very nerfed in this game, so I think any of his abilities like sensing sin might not work on her unless you'd like them to (let me know). He might be able to recognize her as potentially like him, which would be worrisome and confusing for him because she's very different from demons in Good Omens canon.