I come from a long background of indoor coral propagation, so DO is something I've spent a bit of time researching and experimenting on. But keep in mind, I grow in soil. Just thinking you might be able to take something from this.
A few things to start with is that water does have a saturation level for DO, and this saturation level is mostly dependent on temperature. Cooler water holds more oxygen. All gas exchange happens on the surface, where water meets air. The rate at which it is absorbed has to do with the current amount of oxygen and the surface area of water and air contact.
Bubbles don't have a huge surface area, though they do have some. In fact, unless you have a very tall reservoir, chances are the majority if your gas exchange is at the surface. However, bubbles breaking on the surface do agitate the water, which increases the surface area dramatically; chances are this is a greater source of gas exchange than the bubbles themselves (dependent on conditions of course). Another key is to keep the water circulating. The deeper water is the oxygen poor water, so keeping that moving to the surface makes a big difference in net DO. These benefits can be achieved with powerheads as well, and in most situations more efficiently, however other hydro growers have pointed out that powerheads add more heat than air pumps (not much, but a few watts), and in aeroponics you need bubbles splashing roots from what I understand.
As far as providing additional oxy, the only situation I would consider this in would be if you have a sealed reservoir, especially if it is placed in an oxygen poor environment. In normal environments, especially a plant room where you either have good ventilation, or a buildup of oxygen in the light period, taking the above info into account you should not have a problem hitting saturation point for DO.
