Spitoon, mode C information on commercial airplanes is exactly the same as displayed to the pilot as long as the altimeter subscale is set to standard. We can switch the altimetry source for the transponder from left to right and in my outfit it is usually set to report the information from the flying pilot. It is not independent from the two main altimeters on the left or right PFD, the only independent third altimeter on the flightdeck is the standby altimeter.
To use Mode C as a crosscheck is somewhere between useless to dangerous if it instills confidence in the malfunctioning air data computer simply because mode c is still the same as the displayed information.
It is a different thing in smaller planes which have independent blind encoders for their mode c altitude read out where mode c can indeed act as a third independent altitude information.