If someone pays cash and the pharmacy is unaware they have insurance, then no. Cash claims are not reported to insurance companies.
But, pharmacies do report everything they've filled, and this can be looked up so other pharmacies know not to fill too soon, whether someone uses their insurance or pays cash. Unless the pharmacy doesn't check, which people who are trying to fill too soon with cash hope for. But the DEA monitors for things like this to prevent it from happening.

EDIT: People usually go to the doctors and pay cash too to prevent insurance companies catching onto this. I'm not sure how doctors can check if someone is doctor shopping, I've never worked a doctor's office.