Rate of cabin climb depends entirely on how well sealed the entire 'pressure vessel' of the airframe is. I don't think IAS will come into the equation at all.
It was once demonstrated to me on a virtually new airframe at the time (a 747 classic). The training Flight Engineer turned off each of the three packs at FL350When the last pack was turned off the cabin climbed at about 100 ft/min.
However once on an old 737-300 we had a duct split at FL330 and the cabin climbed at about 1000 ft/min necessitating an emergency decent.