Training a dog is more than teaching them a skill, according to my favorite dog writer, Dr. Stanley Coren. Training changes the dog’s brain and alters the thought processes.
In other words, trained dogs are not smarter because of their prior training, but rather they have learned that when they are presented with a problem that has a solution, if they find that solution, they will get a reward.
This was affirmed in a study at the University of Milan. Two groups of dogs were assembled. One group was designated the Untrained Group because the dogs had no formal obedience training or only basic training. The Trained Group had participated in high level training-- agility, search and rescue, retriever training, or musical freestyle performance.
The simple test involved figuring out how to get food from a container in a short period of time.
The results were clear. In the group of untrained dogs only 30% solved the problem and successfully got the food during the test period. However for the group of trained dogs more than twice that number (61%) were successful.
It was also clear that trained dogs were more focused, spending more time working at the problem and less time looking at their owner or the experimenter.
One thing is very clear: high-level training in virtually any doggie skill alters the thought processes and makes dogs better problem solvers. So in that sense you could say that training does make a smarter dog.