It seems that there are hereditary aspects to mental illness. In Bettelheim's case, it might not be possible to determine in what proportion time spent in Dachau or heredity resulted in his illness. However, being in a concentration camp for 11 months would certainly have left him with many mental and physical scars.
Bettelheim's time in the Dachau concentration camp was a contributing factor to his mental illness suffered later in life, because he admitted that he drew on that inspiration for some of his late work. He spent a great deal of his life, 11 months, at the concentration camp. A person cannot do anything for that great of a period of time without it influencing them.
Surely someone spending any amount of time in a Nazi concentration camp would suffer psychological scars later in life. Such is the case with Bruno Bettelheim's internment at Dachau during the Nazi's Holocaust. Although Bettelheim escaped from death in 1939, surely the horrors he may have witnessed at the beginning of the war scarred the middle-aged man for the rest of his life.
As is the wont of the world, there was good that came out of the suffering inflicted on Bruno Bettelheim during his stay in Dachau -- the meeting and ultimate befriending of psychologist Ernst Federn, an individual who undoubtedly influenced Bettelheim later in life. While the experience was undoubtedly trying, it would be a stretch to argue that it eventually contributed to his depression and suicide, especially when considering that men who have lived perfectly ordinary and peaceful lives are just as susceptible. Depression is an indiscriminate killer, and while Bettelheim's past may have been difficult, there was enough good to offset the bad. I would seek an alternative explanation before blaming his experiences in Dachau for his depression and suicide.
I believe it is impossible to say rather the time Bruno Bettelheim spent in Dachau was a contributing factor to the mental illness he suffered in later years. More than likely it probably had some effect. I believe a quote from an anonymous former counselor summed up the real problem with Bettelheim better than anyone else, "What did a forty year old Viennese intellectual really know about the inner (or outer for that matter) life of a ten-year old West Side Chicago Irish kid who had no one to care for him?"