In a DSB, the denitrification uses organics that diffuse into it, either as soluble materials, or as particulate organics (detritus). There is not enough organic material necessarily in aquarium water to get rapid denitrification in a carbon denitrator without adding some carbon. Adding additional carbon to the aquarium might make denitrification in the sand go faster.
Vodka directly into the aquarium will likely mostly reduce nitrate as bacteria in the water column it it rapidly for their own growth. That isn't denitrification,but simple nutrient usage (like macroalgae), but it does work. It may be hard to distinguish which effect is dominant, but I expect there won't be all that much left for the denitrator.
Once nitrates are used by the bacteria in the denitrator, what happens to it as the bacteria dies? So would a denitrator need to be linked with a good skimmer for the nitrates to be truly removed from the the aquarium in the end?
In a denitrator, they are kept growing slowly, and some probably die and break down, but the growth is not nearly as extensive per unit of nitrate consumed as when nitrate is used in the aerobic parts of the tank.
Think of it this way: in the denitrator, nitrate is used in place of oxygen, and also as a source of nitrogen. In the aerobic parts of the tank, it is only used as a source of nitrogen.
While I think skimming is generally desirable, I do not think it a necessary part of a denitrator.