Make sure you do not have a small-diameter copper or plastic tube coiled up somewhere behind the reefer or in the back of an adjacent cabinet - they are frequently run during constrution, just not hooked up under the sink.
Yes to plumber - depends a lot on how hidden you want the tubing, and distance. A simple run through holes drilled in the sides of the cabinets and run along the inside back surface of the cabinets might run $150 or so - running totally hidden in floor joists or taking out bottoms of cabients and running behind the base of them might be the same if exposed floor joists underneath the kitchen, to as much as $600 (about 1/2 drywall repair and painting) or so if not exposed so have to open up ceiling below kitchen.
