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.
Surely the majority of Virginia is still Southern in culture it's just the huge growth and Democratic swing of the non-southern DC suburbs (which are still nowhere near the majority of the state) combined with southern blacks (who do count as Southern despite the rather odd tendency to count everyone not a Republican as not 'Southern') that has made the state lean Democratic. If the DC suburbs were hypothetically not in Virginia it would be considered by everyone an unquestionably Southern state.