No, Barrow wasn't. There is Mark Warner, Joe Manchin, Charlie Crist, and Bill Nelson. They are white Southern Democrats at the federal level in Congress.
Allow me to rephrase that - Last White Southerner in the Deep South, and for most of the Upper South. Virginia has been turned to Greater DC, and Florida is no longer a Southern state south of Gainesville. (But the panhandle and Jacksonville can be considered Southern.) I consider WV to be culturally Southern compared to VA, but I can't exactly decide on how to pinpoint it.