I have seen it done both ways, and in my experience the answer depends on the breadth of the update. If you're doing a complete redesign, then gradual rollout is extremely difficult from a consistency perspective. If you are simply updating the framework (which I realize is never "simple" and will result in some redesign) to work on all screen sizes, gradual rollout would probably work and will help keep your business partners happy.
Either way, you have to be strategic to avoid the changes being too jarring for the user. I've seen it done the worst way possible: a complete redesign done in a phased rollout. This resulted in a brand new pages with brand new navigation systems combined with old pages with different color schemes, imagery, navigation, and patterns. Needless to say, very unsettling to users.