Yes, the internal resistances (also called equivalent series resistance, or high frequency resistance) times whatever current is flowing contributes an "instant" voltage drop that you see in GCD testing, or any other test where current goes from 0 to [not zero]. This is the primary reason for using a constant voltage finish to ensure complete charging of a cell to your desired SOC.

Battery impedance does not depend on any parameters in the measurement, but it is part of the device itself. It can change over time (state of health). That said, it does have an effect on all measurements depending on the magnitude of current being applied.