Depending in the state, the connectivity of the computer in the trooper's car, and the mood and/or ticket quota status of the trooper, you might be ok just by knowing your details. I left my wallet at home once, in my area drivers have 72 hours to produce so I went home, then to the police station and produced it. The desk officer called the issuing officer who said just make a copy of the license and he will cancel the ticket when he gets back. I heard all this over the open radio. "Cancel" in my jurisdiction means it never existed.
In my particular case it was quite beneficial to not have my license as the guy completely forgot to write up the rolling stop that he initially pulled me over for.
However, in your example you will be far away from home, so you can't just go and get it.
Also, there's no car rental company on the continent that will give you the keys without also seeing an original, valid license and supporting documentation from a Vienna Convention country, so whatever the local police think isn't relevant. As you will not have a car you will not be stopped for any traffic violations.