Calculating time-constant with z-Diodes
The actual "r_z of the Zener" in datasheets is called Zzt or the impedance Z of the zener z at the test current e.g. 5mA.

Since this is an "incremental" or "knee" slope on the curve above some threshold voltage, Vth which is just below the rated Vz voltage.

It includes the knee voltage in the equation Vzt= Vth + Izt*Zzt

Your assumption is incorrect  as an ideal voltage source because here it is an incremental resistance only when operating in Zener mode current and not at 0V.  

It would be the same as an ideal battery except only during Charge mode.

When the input=0V , and (Vcap = +), D is no longer forward biased and blocks the zener  with open circuit