Does the 'gas gauge' re-calibration procedure work & make the gas gauge accurate?

not if the bladder is the problem

 

The question presumes that there is a gas gauge recalibration procedure, which there isn't, so a good answer will be hard to come by.

There is a recalibration procedure for the inclination sensors that are attached to the instrument display, and they make a small correction to the gas gauge reading if the car is on a slope. That recalibration procedure does what it says, but you typically only need it if the instrument display or those inclination sensors got removed and reinstalled.