Yes absolutely. Certain aspects of natural selection like the rigid cull system of breeding based on working ability would produce similar results. In this day and age its considered unethical, but was freely practised in times gone by with many hunting breeds. More recently even and up until the ban in hunting with hounds in the UK this was practised with fox hounds. 

Pertinent to Elitegaurdianpresa there is now a show fox hound. A lady in the UK selected hounds that had no disposition to work, bred them and created the show hound. A dog that won't kill your cat. A dog that is useless for hunting too, no matter how hard you try and nurture is previous abilities as a working hound. These are not backcrossed to working hounds or they would make useless pets, instead they are line bred to the those showing the least hunting aptitude. The shrinking gene pool in effect. If true working hounds went extinct these show hounds would end up inbred mutts like all other show dogs.

The most healthy of types are definitely pariah type dogs. Also working dogs that are not bred in closed registries. Even pariah dogs can find themselves in a shrinking gene pool though, same as pedigree show dogs in closed registries. It's rare, but isolation like in some dessert communities for example produces the same results. You will see dogs born and living with genetic diseases and mutations. People too. I witnessed this in some hill "tribes" in Oman in the middle East, the people suffered the same fate due to inbreeding.