It's feasable.
But if you invest 20 bucks on a rear rack from Target and use the backpack for lighter things, you'll be better off. It's not the weight of a backpack that probably will bother you but the sweat and heat it generates against your back. Made my back itchy for a bit until I got used to it. I used a rear rack only and a backpack when I toured this spring from SC to TX.
PS - if you get a rear rack, get one that attaches to the frame, not just the seat post.
Have a nice trip
Cheers,
http://biketour.ne1.net