This is a great and interesting topic! I am an ecologist, and have colleagues who study nitrogen fluxes in aquatic systems. It's very cool stuff whether you are talking about the reasons for the dead zone in the Gulf of Mexico or the processes in a home aquarium.
In terms of the anoxic, denitrification process, my suspicion is at the scale of the home aquarium it would simply be easier to do water changes or grow plants to reduce nitrates. Indeed, I'm not certain it is possible to have denitrifying bacteria perform the function to any degree that would be beneficial (depending on stocking rates, of course).
I'm trying to think of the best way to explain this, so please excuse me if I am fumbling a bit here. For the most part, we try to keep O2 fairly high in aquarium water. This is true not just in the display, but as we run it through filters. Unless that oxygen is utilized by something, it doesn't tend to decrease dramatically (stays in equilibrium with normal solubility with the air). Yes, loads of aerobic processes are going on in our tanks. But to favor denitrification, it takes pretty low oxygen. Denitrification is the least energetically efficient process in the aquarium "nitrogen cycle". That means that the flow of oxygenated water to any given surface must be fairly low, or the O2 is too high and the process is no longer favored. That can be achieved; however, think about if you had to achieve this with your typical biofiltration. Think of the area you would need for beneficial bacterial growth if the flow had to remain low to every surface to achieve conversion of ammonium to nitrate. So, while I think denitrification occurs in all aquaria, the area necessary to deplete the influx of nitrates would be massive, given the low flow rates that would be required to first deplete the oxygen. After running through an effective denitrification reactor, the water would then need to be rapidly re-oxygenated or it would be lethal to the animals in the aquarium.
I am not saying that this is entirely impossible. And as a scientist, I am always eager to be disproved by good data. That said, I remain highly skeptical of the efficacy of such systems (even after watching videos made by certain doctors). Additionally, I am not certain that an effective denitrification reactor would be a better option than simply changing your water regularly, or growing plants (even if only in a refugium). Yes, plants will largely have an affinity for ammonium over nitrates, but they will scavenge nitrates quite effectively (which plants are best for this purpose in a freshwater system, remains an open question for me).