Not necessarily.  A good coach will be able to provide high quality and effective coaching with or without shared experiences.

Shared experiences provide unique understanding and connection which is helpful in coaching, however this could also hinder the process. Both client and coach need discipline to avoid becoming mentor/ mentee.

Where experiences differ, the coach is able to respond with curiosity, from a place of fewer assumptions, and may be better able to bring awareness to blind spots. However, building that connection could take a little longer.

When considering a coach, consider the profile of the coach that may be most helpful for your current goals. To what extent is shared experience essential here? Speak to a number of coaches before making a decision.