No. The monitor itself should not make audible clicks from software changes. The sound is likely from your PC's speakers or a system sound.
DDM uses the DDC/CI channel to send commands. This is a digital signal. It does not trigger physical relays in the monitor that would click. Check your Windows sound settings. Disable sounds for device connection events.
If the click is confirmed to be from the monitor's internal hardware, that indicates a potential fault. Contact Dell support. The monitor may need service.