Yes and no:
Yes, if the complaint facilitates improving the performance of your “no service is the best service” process by rapidly eliminating the root causes of the complaint and precluding similar complaints.
Yes, if the complaint facilitates the education of your customers on how to use your product or service more effectively in the future.
Yes, if the complaint promotes the education of your frontline employees on managing moments of truth in customer service more effectively.
Yes, if your service recovery process can fully recover from the complaint and then some.
No, if the complaint discourages the customer, and her family and friends, from starting, continuing, or expanding a [the] relationship with you.
No, if many more customers leave you silently without first complaining.