Earlier quoted context omitted.
It will still be picked up by a PCR test depending on the number of replication cycles. Which is why mass testing everyone, including healthy people, is such a dumb idea.
Only if the number of cycles wasn't pre defined. Which it is, nobody is running cycles until a PCR test turns positive.
Generally in the past, it was accepted practice that doctors do specific tests to get more certainty with diagnosing certain infections in a patient that's showing symptoms matching that disease. You could make a case for mass testing healthy people for all kinds of infectious diseases but for economical reasons I doubt many would support it. If we did that we'd have to somehow account for all the false positives, then.