Absolutely not!
Although there are some research studies that indicate there is a genetic component to spine and joint health, genetics are not 100% responsible for back pain.
If you are concerned you may develop back pain some things you can do to keep your spine healthy: exercise regularly (strength and cardio), learn proper lifting mechanics, set your work space up for ergonomic success, learn how to move your body (Pilates, Yoga, etc.), eat a healthy diet, weight management, and have a good supportive (firm) mattress.
I love this question because I believe that prevention is the best way to approach back pain (and overall health in general)!