Well, Martha, you couldn't do it on your road bike, but a hybrid or mountain bike would be fine. Great excuse to buy a new bike!
And the more I think about it, I think I'd rather just do a TE ride and not be part of the C&O Association ride. But I'm antisocial like that.
And I think it would be fun to take enough days to do it to soak up a little bit of Civil War history on a few side trips.