The simple answer to this question is maybe. That said, it does the dag have fur, or hair. Hair dogs, like the Portuguese Water dog will felt well especially a curly coat, and will thus spin. Most non shedding dog breed descend from the PWD. Two coated dogs under fur usually will. I make spinning wheels, so have a wee, and I mean wee bit of knowledge of spinning, and have been exposed to a lot of spinners, some of whom can spin anything resembling hair or fur. As a trial you could try felting some of your dogs shed fur.
Woody
Woody