Not necesarily true. Low ph and temperature renders ammonia relatively harmless....
Also you should be doing daily doses for prime. It detoxifies a large amount of ammonia.
I would take the cories out and put them in a spare tank with a sponge filter or something. They will be dandy there. Don't worry about it too much we all make mistakes. I did this recently as well. I thought I cycled it since ammonia was reading 0. Then when I did a water change at my new residence the next day it was 4ppm.