Can I download the PDF report via the API?

Yes.

POST /searches/{id}/export generates the PDF report for a business search, the same report you can download from the console, with the full business profile and every check that was ordered.

The response is the PDF file itself, streamed back to you, so save the response body to disk or forward it to your document store. Use it to attach a report to your own case record or to share a result with someone who does not have console access.