Could very well be, and is easy enough to try... just don't use a fan on the bucket (or don't drill the lid on the sump.) However it was so easy to use a fan on the bucket, that I wanted to eliminate that variable. Remember there were no previous instances of turf in a bucket before, so, many things were in question. Also, being without a skimmer, I was also thinking about oxygen.
Still, try to picture turf on pylings in the ocean. Why is it only at the water level? There is plenty of motion below, too. If air (i.e., co2) is not as important as light, why does the turf not grow all the way down the pyling to the point where there is no more light? I seem to recall that turf on pylings starts right at the water level of low tide, and goes up from there to the point of the highest waves. Also, as for the water being saturated with O2 and CO2, I thought one of the benefits of turf is that it does the O2 saturating itself.
I found the following on one of Aday's online patent decriptions, so you might be right: "Assuming adequate light is provided, algal turf production is limited only by inadequate exchange of metabolites -- oxygen, carbon dioxide and nutrients -- between the WATER and the cells of the attached algae."
http://www.patentstorm.us/patents/5778823/description.html So maybe all the co2 really does come from the water. That might be why turf uses some of the alk in the water (bicarbonate).
It goes on to say "Essential growth requirements for the algal turf, in addition to an adequate lighting source, include aeration and agitation of the water in order to distribute nutrients and to remove any waste products generated." ... "Wave surge action further enhances the exchange of metabolites between algal cells and the water media. The surge generated by the wave action produces a back and forth motion within the growth reservoir, preventing the development of semistagnant boundary layers that occur when a constant flow of liquid passes by a fixed object. (Steady currents tend to pin the filaments in an immobile position and a surface layer of very slow-moving water develops.) By optimizing such metabolite cellular-ambient water exchange, continuous shading of one cell by an adjacent cell is prevented. Thus, in a preferred embodiment, the algae is subjected to an oscillatory water surge."
As for matting down, the turf that has grown for me so far is like hard carpet or astro turf. It does not move at all with flow in any direction. You can even run your hand across it and it won't move. If this is the same turf that the dumping designs grew, then there is no matting... it's already matted. Anyway, it's certainly easy enough to try the media tray sump version without worrying about air. Just lay the screen down in the media tray, and clip on a light. Should take one minute.
And I answered my own question about the ammonia. The same Aday page said: "ATS produce oxygen during periods when the turf is exposed to light and remove ammonia whether lit or not." and "Ammonia, the primary excretory product of fish, is a good nitrogen source for algal turf growth." and "ATS may act as the sole oxygen supply for fish." I was thinking about the removing-ammonia part, because for a FO tank (I'm planning an all-eel tank with no rock and no sand) would need something to remove ammonia, and I wanted to stay away from the balls.
I don't think there is anything that turf does not do.