I would say that a few month of experience getting used to the bike would be important, but as part of that it really will be essential to taking a few long weekend trips where you get an idea of how well your body will hold up to being on a bike for 8 hours a day. Riding a bike is going to be far more demanding on your body than just getting in a car for a long trip. 400 miles a day in a car is quiet easy, but 400 miles on a bike is a very long day, and doing that for 20 straight days is a fairly extreme trip.

Now of course there are the true iron butt riders who do that and more, so it certainly can be done. I just would make very sure its something you can do and enjoy - and I'd give some serious thought to scaling back your plans a bit so you don't end up on the other side of the country, finding yourself miserable, and have a whole lot of miles still to go.