No, this is not a requirement.
In Chöd, the primary elements are view, intention, and visualization; the damaru and kangling serve as ritual support — sustaining the rhythm, attention, and symbolic dimension of the practice — but do not constitute a musical performance in the conventional sense. The sounds are produced in a simple, functional manner and require neither musical ear nor technical skill.
Many lineages emphasize that, in the absence of ritual instruments, Chöd can be practiced entirely mentally or with the voice, and this is often how beginners start. The instruments are introduced later, when there is an understanding of their meaning rather than a desire to 'learn to play' them.