Yes, surface agitation is the most important factor in providing adequate oxygenation.
When I was a kid I always looked at the thousands of tiny bubbles from my airstones and thought they were significantly increasing the oxygen (and other gaseous) exchange and that they represented a greatly increased surface area. I learned here on TFF that that is not the case. Bubbles are not nearly as significant a factor as surface agitation and area is. They do cause some added circulation of the water from below and they can be an added source of surface agitation obviously, but in general, the spraybar or other surface agitation device of the filter is fully sufficient to provide enough gaseous exchange.
Total surface area is significant (discussed recently by oldman47 in another thread here) in that a shallower tank can maintain more fish when the power goes out!
~~waterdrop~~