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Recently got accepted into my school's most prestigious clinic. Is it worth noting that on my resume/cover letter and updating my applications?

Depends on the school and the clinic. How competitive is the clinic and will it give you an experience and skills that will translate to the clerkships to which you've applied? Is the clinic nationally recognized? If something like Stanford's or UVA's Supreme Court Litigation Clinic, than YES. If it is a business entrepreneurial clinic, while maybe prestigious at your school, I'm not sure I see that translating much to say a COA clerkship. If that doesn't answer your question, give us more info.