Not necessarily. Breast reduction can help to relieve the strain on the upper back, neck and shoulders by reducing the weight pulling in these areas from heavy, dense breasts. The pain from fibromyalgia may not respond entirely from this effort as the pattern of pain is often more diffuse and not always due to a defined cause.
Maybe. The back pain you are experiencing from fibromyalgia is not caused by the excessive weight of large breasts, but your back pain could be secondary to both. If this is the case you could expect an improvement. Your provider or surgeon could guide you to whether some of your symptoms correlate with large breasts and if the anticipated amount of breast tissue removed would help you.
Nothing proven. I have patients occasionally ask me to write a letter to justify the health benefit of breast reduction in relieving back pain. Normally breast reduction surgery is cosmetic and therefore not covered by insurance. They hope that the letter will help them get the procedure covered. I am not aware of a single study proving that this surgery significantly results in back pain relief.