I just think the odds of it being limited (except in areas of extraordinarily small turnovers) are slim given all the various sources. I think where added sources help bacteria isn't in that organic C is limited, but rather a more readily metabolized source is limited. That is where I feel one of the whole ideas for organic carbon dosing is somewhat flawed, but that is a different story.
I don't think I've done a great job of explaining this. Carbon is likely not limiting for growth, but growth is not the largest sink of nitrogen on the coral reef, denitrification is. But denitrification only occurs where there is a source of OM available for that metabolic pathway. If there are low levels of DOM that make it to the sediment, all of it will be consumed aerobically with none left over for denitrification. This occurs in general via the rate law R1 = k*DOM*[O2]/([O2] +KmO2), where KmO2 is the half-saturation constant of oxygen and is around 20 uM (normal O2 concentrations are 220uM). The value of k can vary (and has to do with the availability of the carbon source that you mentioned), but for many aquarium food sources, it can be on the order of 1e-5 mol/(m^3*s) (which is really fast). Since we're talking the math, I'll say that the rate for denitrification is similar: R2 = (k*DOM - R1)*[NO3]/([NO3]+KmNO3). What this basically means is that DOM left over once oxygen is depleted can then be used in denitrification.
Ok, that's all well and good, but it's so far pretty meaningless. Let's consider our sediment, where oxygen and DOM both diffuse at generally the same rate (they don't quite, but it's pretty close). If the oxygen concentration is much higher than the DOM concentration, then the value of R1 is basically always going to be k*DOM (because [O2] is much larger than KmO2 so that [O2]/([O2]+KmO2 = 1); all the DOM will be consumed aerobically, which ends up producing nitrate as an end product. If, on the other hand, DOM is a good bit higher than [O2], then R1 will be less than k*DOM when oxygen levels get low, which means there is now DOM left over for denitrification to use.
That's what I mean by saying DOM is limiting, and I've run a number of model simulations to test the idea; sure enough, under light feeding conditions, nitrate reduction never happens. The model was run assuming a constant input of 1 g of food into a 40 G tank, which is a lot (in the budget, coral production is largely contained within the colony...it's a simplifying assumption), and the sand bed remained entirely oxic.
Now, is the picture that simple? Lord no, and I'm still working on calculating it out without frying my MacPro. Bioturbation (the physical movement of OM) plays a huge role, as does production within the tank. But given the potential for huge, effective skimmers and organics removal, it's not a stretch to see how DOM can indeed limit denitrification. And then the picture gets still more complicated when we consider the energy budget as a whole. Dosing carbon can be an excellent thing to do, it just needs to be done within a framework of knowing how the ecosystem works, which is something I'm working on modeling.
Hopefully I didn't get overly technical, but this is my research, so let me know if you have questions.