Your right, adding fish wouldn't throw out the cycle,
but it will put them at immediate risk of death, disease and shortend lifespans.
Poor water quality is one of the major caurses of stress in fish, and raised Ammonia and Nitrite would constitute a water quality issue if fish are in the tank. Stress leads to lowered immune systems, and hence increased disease suseptability. Couple this with the fact that both Ammonia and Nitrite are toxic, even in small ammounts, and you see where the death comes in... Ammonia (and prolonged exposure to Nitrite) will caurse permanant damage to the gills and other organs that the fish has, and this leads to a shortened life span.
The long story short is that while you could add fish now, and the situation would be
marginally better than throwing them into a new tank, since the cycle is still underway, the fishes wellbeing would still be a major caurse for concern. Wait for Ammonia and Nitrite to be at zero for a full week without waterchanges, while still adding food, before you add fish. This will ensure water quality in the tank once they are in is as good as possible, and hence reduce the risk of problems
All the best
Rabbut