I don't think it's a stupid question.
I would think that the answer is YES, as long as there's enough moisture in the tuboprop's exhaust streams and it's flying high where the air temp is cold enough to make the moisture in the exhaust gases condense into visible contrails. There's probably a lot of turboprops overhead of us everyday that are leaving contrails, but we don't see them because they disipate to quickly.
Back in 1989/90 I lived in Winnipeg, Manitoba where it gets extremely cold outside during the winter. It's normal to have an outside air temperature below -30 degrees C during the daytime in February. One day, I remember seeing a little Cessna 150 flying around 800 feet over me on a very cold (about -32 C before the windchill) clear, sunny day, and it was leaving a thin white contrail that was around 40 feet long! I thought that was very neat to see.