Yes. Place the video on both the video and the overlay tracks in sync with each other. Apply the blur affect to the lower clip and use the Cookie Cutter effect to "punch a hole" through the upper clip. You'll then see the blurred image through this hole. Adjust the size and position of the hole to match the area you want to blur.

If the area moves around you can use the Begin & End options to move the hole to follow the motion. Unfortunately this only allows a single straight line. If the area moves around more than that you'll have to split the clip every time the motion changes speed or direction and set new Begin & End parameters.