If you're asking this seriously, then yes, they can, because all their gills do is filter out the air through the water they take in and get rid of the water. If it doesn't work quite right (and this does happen), the fish can't breathe and dies breathing water for real, and by definition they drown.
Keeping in mind that water alone can, and often does, dissolve into H+ and OH- ions, it is safe to say that a sample of pure water will not create any pure oxygen.
Water normally contains a certain amount of dissolved oxygen, often excreted by aquatic plants, but it could also come from dissolved O2 molecules from the air.
If you put a fish in a sample of oxygenated water, with no plants, and no access to normal air (You may have to fill the container partially with a noble gas.) then there will be no oxygen in the water for the gills to filter out.
So yes, you can drown a fish if you remove the dissolved oxygen from the water.
