Research suggests that personal attributes and skills of therapists such as sensitivity, genuine concern for others, and intelligence have a greater impact on treatment outcome rather than therapeutic modality. These skills often come from life experience. Therefore life experience is important for a therapist to be effective, but the question remains, must they have the same experiences as their clients?
The answer is NO. The ability to empathize is the foundation, cornerstone of all effective therapy. Part of the definition of empathy is the ability to feel someone's pain and communicate back to them in words that understanding. Someone who can empathize does not need to have experienced the exact same disorder, trauma, experience as the client--they need to be able listen to the client from their perspective and process what the client is telling them (and at times draw from their own, similar pain). Also noteworthy is the fact that some human conditions are marked by a lack of empathy for others, therefore these people would definitely not make good therapists.
Self awareness (including issues of counter- transference --how the client affects the therapist) is critical for good therapy. Therapists who are not self aware tend to make comments out of their own issues, rather than stating something therapeutic. Therapy for therapists is a crucial part of training, so that the therapist can separate out their own issues and feelings from that of their client's. While experiencing similar things/disorders as clients can be helpful, it can also cause disaster if the therapist has not worked through those issues.
Interpersonal Process in Therapy: An Integrative Model Edward Teyber, Faith Holmes McClure (This is a secondary source, but the primary sources are cited in this book).
The Social Neuroscience of Empathy by Jean Decety
Kottler, J. A., & Carlson, J. (2002). Bad Therapy: Master Therapists Share Their Worst Failures. New York: Brunner/Routledge.
Kottler, J. A., & Carlson, J. (2006). The Client Who Changed Me: Stories of Therapist Personal Transformation. New York: Brunner/Routledge.