GLUEBALL
Physics and maths apply to both unpressurized and pressurized airplanes.
If you have to lower the cabin (pressurized or not) from say 7,000 ft to sea level, the rate at which you do it depends solely on the time it takes, that is: the elapsed time since the TOD to touch down.
No matter if you use the most sophysticated pressurization system or are in a cessna C172.
If, instead of beginning descent at the computed TOD, you wait ten minutes and then you make an emergency descent at MMO/VMO with speedbrakes extended you will have very high a cabin V/S because the system has to reach sea level in less than half the time it had planned for a comfortable cabin rate. The rate will be twice as much!
Besides, you would probably "reach the cabin" before landing.