The short answer is yes, as the people of Galicia fall under Spanish law. But they are designated as an “autonomous community” of Spain and they clearly think if themselves as Galician versus Spanish. Galicia is located on the NW part of Spain and is most famous for its city, Santiago De Compestela, the end of the 5 designated Camino pilgrimage walks.
The Galician language is closely related to Portuguese, both of which had virtually the same history until the middle of the 16th century. Despite a divergent history since the Middle Ages, even today Galician and Portuguese are mutually intelligible almost without effort. As well the standard Galician pronunciation mirrors much of Spanish.
Spain is divided into 17 parts called autonomous communities (designated in 1978). Autonomous means that each of these communities has its own executive legislative judicial powers. These are similar, but not the same, as states in the USA, for example.
