Not necessarily. It is possible to overdo it.
Water intoxication, or hyponatremia, a serious condition when blood sodium levels drop precipitously, can be caused by sweating excessively over several hours and drinking way too much water (versus a sports drink) while not eating or urinating (which often slows during intense physical activity).
This could happen to someone who engages in a long athletic event (e.g., a marathon or several day hike). Symptoms include confusion, disorientation, weakness and nausea. Hyponatremia can lead to seizures, coma and death without prompt medical attention.