They probably did. Here's a good few captured examples: German Warplanes 1939-1945, Captured Allied Aircraft in Luftwaffe service Among them we find that:
A Fairey Swordfish was maintained in serviceable condition for around six months, one has to ask why.
A special squadron went around training front-line squadrons against them, not sure if you'd regard that as "operational", but it is more than mere test and evaluation.
Several examples are transports. It might seem unlikely that these were never used in their intended role.