Nothing is actually being oxidized, the water is becoming more oxygenated — more dissolved oxygen. Plants and microbes both use it. But they'll use it up if it's not replenished. They are literally "breathing" it and "exhaling" CO2.
A lot of the "action" in soil goes on in a micro-thin film of water that coats particles and root surfaces. Oxygen and nutrients have to be dissolved in that soil water or the roots and microbes can't get it.
Oxygen and other gases do not diffuse through water quickly (about 10,000X more slowly than a gas diffusing through a gas), but if you have thin films of water coating soil particles and roots, the oxygen in the soil water is quickly replaced and everybody, roots and microbes, are happy.
When soil is "heavy," without a lot of large pore space where air and water easily move, the water isn't just present as thin films on soil particles — it's a "thicker" mass of water and it takes a long time for oxygen and CO2 to pass through. This is why perlite or some other substance is added to soil mixes — to allow easier exchange of oxygen and CO2.
When soil dries, what is happening is the water in the pore space is being replaced by air. My thought was that if your oxygenated water provided enough oxygen for the soil biological community until drying allowed more air in, it could be beneficial.
This will be an experiment. Obviously the easier way to go, next time, will be to add more perlite to your soil mix.
