No.  Varicose veins are caused by failure of the one way valves in leg veins (venous insufficiency).  This allows gravity to pull blood back into the leg veins in reverse direction.  This abnormal hydrostatic pressure can lead to varicose veins, aching, swelling, night cramps, numbness, and other symptoms.  Risk factors for venous insufficiency are hereditary, female gender, pregnancies, and vocations with prolonged standing or sitting.  While physical activities such as running or walking temporarily propel blood in the right direction, it does not have a lasting effect.