It really really depends on the type of nute and the amount. I'm not a finicky fish keeper; I don't monitor water conditions, have an undersized filter, but I have massive amounts of dirt and plants in my tanks that operate as a massive biological filter - very similar to the algae they use in
the very last/one of the latest stages of waste water processing (where the fish reside to eat the algae - they themselves are not part of the filtration) - this process is after several mechanical separations of waste and then several steps of biological filtration via bubbling pools. The amounts the EPA allows of Nitrates at this stage or water filtration is 10 ppm, maximum for fish being around 100ppm with ideal conditions being below 50 ppm.
Typically the algae stage where the fish reside would be after disinfection on the way to discharge:
Much of your fertilizer will be nitrites (not nitrates) which the fish are MUCH more sensitive to with a tolerance of only 1ppm and ideal ranges being around .1ppm. Most hydro growers I know try and run at around 600-1200 ppm which should easily kill any fish. Aquaponics is VERY VERY different than putting an algae eater into a dosed res.