No. Because there isn't a sensor in the standard system that measures air pressure.
You could buy one, it's called a pressure transducer, but they can be fairly expensive.
The best you can do is check if the pressure switch has been tripped to see if it thinks more pressure should be pumped or not.
Pretty much we can only trust it to indicate:
- OFF = pressure has been at 120psi recently and it hasn't yet dropped below 95psi
- ON = the pressure is not 120psi