No. An individual blood cell will complete the whole loop but can take any route through the circulatory system to do this. For example, a blood cell leaving the left ventricle may immediately pass throughout the coronary arteries to supply the musculature of the heart or alternatively could carry on down the aorta. Another cell could be swept down the subclavian artery to the arms and back through the corresponding veins, whilst another could follow a route through the external iliac arteries to the legs and back through those veins.
That being said, _all blood cells_ will pass through the central elements of the pump _every cycle_. These are the right atrium, right ventricle, pulmonary trunk (common part of the pulmonary artery), the left atrium and the left ventricle.
Other than these locations, the movement of blood cells will be random.