No, three electrodes configuration for cyclic voltammetry experiments are arranged in such a manner that reference electrode is chosen for SCE (Saturated Calomel Electrode) or Ag/Ag+ reference electrode whose electrode potentials are known. Counter electrode chosen is always an inert electrode where there is no interference of the material encapsulated on working electrode. Working electrode is taken either as such or if redox behavior of an unknown compound  is to be determined, then Pt or Glassy Carbon electrode or ITO can be taken. For determination of redox potential, potential window plays a major role and one must define the potential window.

Purified water is never used for doing any electrochemical reaction. Some electrolyte has to be present for the conductivity in the system. KCl can be taken as an electrolyte in water or depending upon study requirements even 0.1 M H2SO4 or HCl can also be taken.

That's reasonable and make a total sense for CV measurements, but what do you think if we just would like to measure the impedance of the purified water using an Electrochemical Impedance Spectroscopy, EIS? wouldn't I be able to just measure the Rs as my Electrolyte(purified water) resistance? 

Sometimes we performed the EIS measurements in 3.5 % NaCl or 1.0 N HCl. But for studying corrosion inhibition phenomenon, we took deionized water for studying the corrosion behavior.

I think you could try to do it. To be on the safe side, before and after the experiment you should measure  the open circuit potential of your reference electrode vs. conventional reference electrode. To check if the ocp doesn't change. In the case if the ocp stays the same, your reference electrode mot likely wasn't polarized.