No. Not at all. Completing DMAIC Or DMADV project undoubtedly will give great confidence for any professional in this field. The "Hands on experience to say". Such an experience is definitely required and will be an added advantage while hiring improvement manager in any organisation.
However, question here is "Is it essential or mandatory that the candidate should have completed the DMAIC Or DMADV project?" then the clear answer is NO.
Role of Lean Six Sigma Black Belt professional as an improvement manager demands that the candidate should be able to identify the right kind of projects to begin with and then mentor both function specific and cross functional projects involving varying level of skills - Leadership, communication, interpersonal (Soft skills) and also rock solid knowledge base - not only on DMAIC or DMADV but also on several other aspects like maturity and ability to understand the business in totality - "vantage" which is built over years of experience.
Completion of one or two Six sigma projects may not qualify or ensure that the candidate is fit for the role of improvement manager. However, it could be an added advantage to some deserving candidates when assessed for the role.