Can I scan using a CanoScan 5600F without a driver? There is currently no driver for OS Catalina.

No, that will not work. Canon has decided to stop supporting Macs. I would strongly advise trying VueScan. It supports hundreds of scanners including many Canon models.

The CanoScan 5600F is supported by the paid, non-subscription, 64-bit VueScan without any Canon drivers or support software. True vendor independence.

If the scanner is on the network - some devices have a web page that you can use to scan and download the PDF from. Just an idea.