I think it's a possibility. The PCR test may be picking up viral RNA that the human cell transcribed from the integrated SARS-CoV-2 gene. But this is assuming that the transcribed gene is not harmful to the host. And also assuming that the cell culture results translate to living organism.

But I also think there's no better cost-effective option that the PCR test to confirm COVID-19 diagnosis. So, as with any other tools, I think there will always be tradeoffs.