Ammonium
is toxic to fish (and to other animals). Not only do I not believe otherwise even if I hear it from a biologist/chemist, I will question anything said by that biologist/chemist afterward.
Ammonium is produced as a waste product by fish. The reason it is a waste product is that it is harmful to the fish. In most creatures other than fish and aquatic inverts, ammonium is turned into urea, because urea is
less toxic than ammonium, and thus can be stored within the body for a longer period of time (fish don't have to worry about this, because they can just excrete their waste as it is produced).
To give you an idea of the toxicity of ammonium, look at the statement that urea is less toxic than ammonium. Now think about this: urea is the product in hair-removal products that causes the loss of hair. If you leave these products on your skin for 10 or more minutes, you will likely get blisters. Our skin is a far cry more durable than our fishes' gills, and they're left to swim in a substance that is more toxic than this stuff that causes us to blister in 10 minutes.
Now, granted, the urea in hair-removal products is in higher concentration than the theoretical ammonium in our aquariums, but it also is only in contact with us for a matter of minutes, rather than the 24/7 that we're talking about in the "never cycle the tank" scenario.
To further dissuade this idea, let's look at this: To have a pH of less than 7.0, you likely will have very soft water (very little mineral buffer). When fish waste, plant
detritus, and uneaten food breaks down, it creates a mildly acidic substance. This isn't a problem in most cases, but in water with little mineral buffer, this can precipitously drop the pH, causing severe harm to the fish.