Not impossible. In fact, its fairly common for scanners, especially document imaging units (what we used to call copiers) to out to PDF format in addition to JPG, GIF, TIFF, BMP, etc... Both my office Ricoh copier and Canon desktop scanner not only provide output to PDF but also the option to perform in-line OCR.
Current OCR and crawling technology is truly amazing. Our enterprise search crawls, in addition to full text search on Office documents and PDF's, also performs full text OCR on image files. You might expect a CAD drawing to be indexed but it also will OCR a JPG or GIF, "sense" text, and index the content accordingly.
Can you tell I'm an IT guy? Jeez...