I realise there is lots of oxygen in the tank water, but in comprison with something similar to that and a trickle type system, the trickle type system is going to house 20 times as much nitrobacter then the tank water.
In other words, the production of Nitrate from a small internal submersed powerhead filter, (If stupidly used for something else), will produce such a small fraction of nitrate IMO, that it would be barely noticeable on the grand scale of things when it comes to Nitrate production.