I'm an American citizen living in Germany since January, 2019. I have/had a valid Illinois (U.S.) driver's license. In Germany, residents with U.S. driver's licenses from certain states can apply for a German driver's license by surrendering their U.S. license.
I've done just that, and in exchange for surrendering my license I received a document from the German Führerscheinstelle which has a photo of my Illinois license, and it basically states that I surrendered the license to them. This document allows me to continue to drive in Germany on the authority of the Illinois license (up to the German 6 month limit anyway) until I receive my German license in the mail, which has not happened yet.
I want to take a little road trip next week through Austria, Liechtenstein and Switzerland. The question is, can I legally drive in those countries as a visitor, on the authority of my Illinois license, even though I don't actually have the license in my possession - just the document from the Führerscheinstelle? (I'm aware Switerland [and Liechtenstein, thanks @phoog] are not EU members and wouldn't be surprised if the answer is different than for Austria.)
(If it matters at all, I'd be driving a German-registered vehicle which I own, I have a valid International Motor Insurance Certificate, and I'm aware of the need to purchase Austrian and Swiss motorway vignettes.)