Once the initial start-up phase is over and the engine is running, all systems are driven off the alternator and what is left is used to top-up the battery. The internal regulator in the alternator adjusts what is supplied depending on the demand.
The alternator output @ idle is sufficient for the PAS to operate without killing the battery, as you said yourself- if the battery voltage is weak, the PAS will operate sporadically. So therefore (if the system is really on it's knees @ idle) and the theory is correct, activating the 'CITY' mode will see the PAS shutdown. But it doesn't, because there's enough reserve capacity in the charging system to cope with the intermittant demands of the PAS.
Fiat would look pretty stupid if the charging circuit couldn't handle the 'CITY' button being used when stationary (as it was designed to do- providing extra assistance when manoevering slowly/stationary).
People seem to think pressing the 'CITY' button instantly increases the voltage/current delivered to the PAS motor- it doesn't. It merely alters the point at which the assistance begins (for a rough example, when only 3Nm of torque is sensed instead of 6Nm). It's only for that very short period when the steering is turning and the resistance load is against it, that the motor is supplied. Once the steering movement is stopped, or the vehicle is moving (which decreases the resistance to turning and therefore the torque felt by the column) the voltage/current supplied to the motor is zero.
T and myself have worked on hundreds if not thousands of Punto's over the years, and agree that there is no correlation between usage of the CITY button and the lifespan of the column or battery.