No. While the villains of the film are corrupt Union soldiers, they attack Josey and murder his family. This prompts Josey to join up with the Missouri Guerrillas until they are disbanded. Josey himself isn't shown to have any political leanings. But he certainly wasn't going to join the side that his family's killers were on.
It should be noted that the author of the book the film was based on turned out to be a devout racist. However, Eastwood was unaware of this when adapting the book in to the film.
