Only if the area changing is near the start of the search, not near the goal. (i.e. near the sensors of a mobile robot, rather than near the destination far from the robot).
D* can be pathologically slower than repeated A* searches under such conditions.
I've been using a modified D*. It increases the grid size as the path moves out of the robot's observable area. This allows a fast search even when the goal is in a environment with known dynamic obstacles.
Ideally speaking, you need to plan in higher dimensions to get an optimal path in dynamic environments
D* can be pathologically slower than repeated A* searches under such conditions.