It is definitely possible to consume too much fluid before, during and after exercise.  Remember also that hydration is a measure of fluid in the blood stream not in the stomach.  If you lose too much sodium in your sweat it becomes difficult for the body to pull fluid from the gut into the blood stream.  There are cases where people will consume vast amounts of fluid only to have it reside in the gut.  People who experience this will feel bloated and may even start throwing up.  This is one of the reasons sports drinks contain sodium.  Sodium will move from the gut into the blood stream causing an osmotic gradient that effectively allows water to follow.

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