I don't think this is something that you can figure out just by sitting down and thinking about it. It's something you'd have to setup a carefully designed and controlled experiment to determine.
That being said, I don't think the conversion of waste to ammonia, nitrite, and then nitrate occurs at a high rate. The concentrations are relatively low and I think would be distributed evenly throughout the entire body of water. There isn't a plume of nitrite, for example, streaming from the filter. I don't think you would find any difference in ammonia/nitrite/nitrate levels before or after the filter or any stages of filtration. You'd have to slow the flow rate to almost zero for any step of the nitrogen cycle to become localized. Think about how long a filter has to be deprived of flow for detectable levels of hydrogen sulfide to build up. Even the slightest flow would prevent that.