I may just be incompetent, but what are BARs?
Springfield armory is still in existence the one described in the book would match up with the model 03. The Tredgar is fictional as a company but it is based on the Enfield for the early bolt action model.Thanks, Oz.
And to awnser your question: no. The United States fought with a new bolt-action Springfield Rifle, and the CSA used a Tredgar. (Both fictional, i think)