Based on the following paragraph on drinking water, is there a risk of drinking too much water during exercising?

The human body contains from 55% to 78% water, depending on body size.[90][user-generated source?] To function properly, the body requires between one and seven liters (0.22 and 1.54 imp gal; 0.26 and 1.85 U.S. gal)[citation needed] of water per day to avoid dehydration; the precise amount depends on the level of activity, temperature, humidity, and other factors. Most of this is ingested through foods or beverages other than drinking straight water. It is not clear how much water intake is needed by healthy people, though the British Dietetic Association advises that 2.5 liters of total water daily is the minimum to maintain proper hydration, including 1.8 liters (6 to 7 glasses) obtained directly from beverages.[91] Medical literature favors a lower consumption, typically 1 liter of water for an average male, excluding extra requirements due to fluid loss from exercise or warm weather.[92]
Healthy kidneys can excrete 0.8 to 1 liter of water per hour, but stress such as exercise can reduce this amount. People can drink far more water than necessary while exercising, putting them at risk of water intoxication (hyperhydration), which can be fatal.[93][94] The popular claim that "a person should consume eight glasses of water per day" seems to have no real basis in science.[95] Studies have shown that extra water intake, especially up to 500 milliliters (18 imp fl oz; 17 U.S. fl oz) at mealtime, was associated with weight loss.[96][97][98][99][100][101] Adequate fluid intake is helpful in preventing constipation.[102]

Yes, since exercise induced stress can reduce the volume of water that the kidneys can excrete, drinking too much water during exercise can result in water intoxication which can be fatal.