How would they be? None of the vaccines available in the United States use the original virus. The segment encoding the S-protein does not trigger RT-PCR. You can’t get COVID-19 from any of the vaccines. You can’t trigger a positive COVID-19 test because you’ve been vaccinated.
This is very different from a serology (antibody) test. That WOULD trigger positive after vaccination, but no state uses serology testing because it’s not intended to discover active infection, but rather to demonstrate that someone has been exposed to SARS-CoV-2 (or a vaccine) in the past. RT-PCR will only trigger on the actual presence of SARS-CoV-2 at the point of collection (typically the nasal cavity).