Yes, very much so. Regional accents in the future U.S. were mentioned in surviving literature at least as early as 1739. In all likelihood, regional accents had existed for some time before that.

For the Civil War specifically, you may be interested in this earlier answer of mine. It's a two-parter. About halfway through the first part, it discusses the South at the time of the Civil War, and then after some follow-up questions, if you scroll down, the second part deals with the North. There are audio/video examples provided there, of actual Americans who were alive during the Civil War, and who lived long enough to have their voices recorded.

I don't mean to step on anyone else's toes. More can always be written, and perhaps somebody else has some further historical knowledge to add.