In the sense they were created as a breed for hunting rodents, yep! "Pinscher" refers to breed used for hunting small game or guarding. They were part of the terrier group when they first were part of the AKC.
My former dog was purebred (with no chihuahua in his bloodline) and it was crazy to watch him in groundhog fields. The min pins seem to be a little more of a problem solver and create traps for vermin rather than just flushing them out and chasing. We didn't let him actually catch anything but he sure did know exactly how to collapse tunnels and leave only one exit point!
Doberman Pinschers were created later, also from the German Pinscher, but I think most historians believe they were mixed with Rottweiler and Black/Tan Terrier to get the same coloring as the Min Pin. They were created as a guard type dog.
I had NO clue about any of that when I was given my first min pin, but worked for a vet that had some really cool textbooks about breed history and health issues. It explained why my dog was always hiding things in holes and the couch and under pillows and in clothes in the closet and then hunting and "killing" them later