Not really. Most of the gas exchange happens at the surface. The bubbles make the water move, which brings stale water up where it can get some oxygen. But when the bubbles break at the surface they cause some agitation, which increases surface area, thus enhancing gas exchange.
They move so fast through water that not much oxygen has a chance to be exchanged while they rise. If gas could exchange like that, then CO2
bubbles that size would dissolve instead of mostly going into the air. That's why CO2
has to be broken into extremely fine bubbles or otherwise slowed down so it will dissolve before it reaches the surface and gasses out.