The only place I could see this being a problem is in a case of Old Tank Syndrome (OTS). A high enough nitrate concentration will eat away at the natural buffer, causing the tank water to acidify to levels possibly below pH 6.0. This is usually a gradual buildup over time (generally due to neglect/lack of water changes) so the fish can usually adapt to the high TDS levels in the water column.
Eventually, however, the pH drops enough that the nitrifying bacteria are no longer able to live, so the colony begins to die off. This is what eventually leads to the spikes in ammonia and nitrite. This happened to the tank at my parents house, due to almost a complete lack of water changes.
Note that nitrate levels need to be off the charts for this to happen...somewhere in the 150-200ppm range. If this buildup occurs over the course of several months, the fish will adapt, although its certainly not healthy. It won't however, be the case if we're talking about much lower levels of nitrate, in the 20-40ppm range.