Simple answer, no.
Water will hold disolved oxygen (DO). How much depends on water temperature, water quality (disolved solids like salt and such). The warmer the water the less DO it will hold, and colder water will hold more.
Now if there is extra oxygen in the water, it will just release into the atmosphere. If someone knows better please correct me, but fish are happy with as much disolved oxygen they can get.
As a side note, on the fish farm we monitor DO levels religously. If the amount of oxygen gets too low, below 5ppm, we stop feeding the fish; a fish digesting lunch consumes more oxygen then a fish going hungry.