My own experience - I had cyst problems in my teens, particularly my left ovary seemed to hurt so much, I could barely walk at times. I had my first laparoscopy at age 19. All they told me was "cysts." Since then I've had 3 children, gone through menopause and I'm fine. Last year my left ovary decided to act up again, grew another big old cyst (not willing to give up!) and I had the ovary/cyst removed. But no cancer. That's how it all worked out for me.
I don't believe there is a connection.