The solubility of H2 in water at room temperature and pressure is 1.6 PPM so you are not going to get much hydrogen out of any drinking water. As an example, 1 L of water has 1.6 mg of h2 max. If on the other hand, If it is as a hydroxyl then all that happens is the water is alkaline. Pure crap I am afraid.
The concentration of hydrogen in the atmosphere is about 0.5 ppm so your heavy breathing as you exercise will get you way more hydrogen than the water, depending on how much of the inspired hydrogen is absorbed.