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.