If the tank has very low nitrate, population would become limited by nitrogen availability. However, I highly doubt that any tank with fish can become nitrogen limited. You might not measure high concentrations of any of the nitrogenous waste products such as ammonia, nitrite or nitrate because as soon as these compounds are produced they are consumed by bacteria. The nitrogen in these compounds is either incorporated into new bacteria or converted into another form of nitrogenous waste. This is what we call nitrogen cycle.
Under these conditions, if you have a considerably large bacteria population, it might become phosphorus limited. However, the elemental composition I posted show there is a much lower phosphorus demand compared to nitrogen. This is why carbon dosing first reduce nitrate amounts and after some time phosphate levels start to drop. You need a larger bacteria population to consume all that excess phosphate.
So it all comes down to balance. If you very few fish and feed so little, your tank might become nitrogen limited for bacteria (in my opinion this is very unlikely to happen). For some reason if you have higher phosphorus (like from rock leaching or from water), your tank might not become phosphate limited as long as there is far less nitrogen since the demand for nitrogen is higher compared to phosphate.
). So every feeding is carbon dosing at some extend.. However, stuff that corals eat such as copepods or rotifers do can feed on bacteria. So carbon does indirectly move to the other larger members of our tanks. However, also consider the fact that most of the carbon probably moves outside of the system as carbon dioxide. So only a fraction of the added carbon would end up in something visible to naked eye.
