The short answer is yes.
The long answer is:
Any time a zener shunts voltage, particularly zeners rated above 3.6V (<= which is true zeners ... but that part's complicated), it will create noise, because it must dissipate heat.
You can help keep the zener and the circuit happy by determining the current draw of the circuit, and then putting a current limiting resistor before the zener such that you will drop the voltage BEFORE the zener shunt to as close to the zener's rating as possible under normal conditions. If there's ever a situation where the zener is asked to do more of it's job, or if the wrong polarity is hooked up, then the CLR will help keep it from blowing up as well. You have to make sure you use a high enough wattage for the CLR. Start with Ohm's law, and you'll naturally be led to the formula you need for the second part.
While the noise increase is a real thing, you are unlikely to notice unless it's a very high gain effect and a very quiet rig.