nevin, I do it all the time. The rub, as far as I can tell, doesn't penetrate the meat, so it's just adding surface flavor. The brine is helping make a more tender, juicy bird.
BUT - I do not put salt in my rub!
I follow Cook Illustrated guidelines for brining and have never been disappointed. My family is always amazed when I smoke. I brine my bird, remove it and let it air dry, then add a rub, and in the smoker she goes. Of course, it works on the grill, too.