I live on Capitol Hill and ride through Vienna going the other way. It's a beautiful ride. Traffic is going to be worse in the afternoon, even going against the major flow. The area around Penn and Minnesota, before crossing Sousa back into Capitol Hill is crazy; cars making uturns in heavily congested areas to avoid waiting in line to get onto 295. I see bikes on Sousa a lot, so it's definitely doable.
Have fun. And if it gets too exhausting, you have the option of the Metro in the morning.