The short and quick answer is yes the tank will cycle right away however your fish will be apt to die if they don’t they mediately from shock. Another issue is stress related diseases such as ich, fin and tail rot, swim bladder issues etc.
It would be the same as if you were trapped in a small confined space had only 4 yds of oxygen to breathe for several hours, you will survive but afterwords to be more susceptible to stroke, heart attack, pneumonia and other ailments that would appear besides PTSD.
Whats the horraible hurry? Why bother stressing the fish when you could let the tankcycleproperly. It won’t hurt them to stay in a pail, jar or bucket as long as it’s oxygenated for the duration of the cycle.
My son killed off a tank of over 150 fish, hw managed to drop a pound of food in the tank, transferred the fish into a pail, did an emergency breakdown of my tank then filled it using filtered water, distilled water, well water and bottled drinking water, he forgot two important things, first was the water treatment and tthe sting the other was to match the temperature. He managed to cook the whole lot of them, the tank was 94 degrees, the ucket was 68 degrees. His excuse was he used the super filter in the tank with “activated charcoal” but didn’t read the directions that it took 72 hours to cycle all 300 gallons.
U can try and force the fish into the tank however don’t get upset if they all die or get sick.