While the fish may appear fine, ammonia usually affects the gills. On something as small as a neon tetra, the gills really aren't visible, so you have no way of knowing what damage was actually done.
For example, they may be fine in fully oxygenated water, but let's say they did sustain some gill damage during the cycle. If your filter goes out/whatever event is necessary to stop surface agitation in your tank, they could be at a greater risk of suffocation because of their reduced ability to extract oxygen from the water on top of the fact that the oxygen concentration in the water is decreased.
That's why I wouldn't recommend this method.
Edit: when I say "this method", I mean a fish-in cycle without doing any tests or water changes. In general, I think fish-cycling is ok as long as you're vigilant about keeping ammonia and nitrite down.
Joseph Granata