No, they don’t output pack voltage until the taper portion of the charge.
The first part of the charge cycle is constant current which means that the voltage varies in order to keep the current the same. The voltage is raised to increase the current flowing into the pack. The only time that the charger voltage is the same as the pack voltage is when the charge current is zero.
While I haven’t done the math, 600v sounds completely reasonable to me for 120kW.
The voltage the pack is at, not the max pack voltage.
For bulk charge, the SC output voltage is :
(Pack voltage with x amps charge current) + X*(round trip cable resistance)
For taper (constant pack voltage):
(Pack max voltage) +Y*(round trip cable resistance)
Guessing at taper, the car tells the SC the desired current (Y) to achieve the desired pack voltage.