Yes, they should verify the information with their reader. But many wouldn't.
I'm Ukrainian, we've got a government app called Дія, that contains a digital copy of ID card, driver's license and some other documents. The document is presented in text+photo form (which is obviously easy to fake) and in form of a QR code that has a TTL of 3 minutes. Police is supposed to scan the QR code with the same app on their phone and that will load a copy of the document from government server, which is a way to properly verify the document.
Still, on my last interaction with police, they just took a picture of my phone screen. It would take a bit of time to train all personnel on using digital documents.