Can breast reduction surgery help reduce cyclical breast pain?

The answer to your question is possibly. Generally with significant reduction in the volume of the breast the symptoms improve.

In theory, since a breast reduction will remove some of the breast tissue that is causing pain, it may possibly reduce the amount of pain you experience. I do not think it will ever completely eliminate your pain as you still have breast tissue remaining. 

You have asked a good question and a breast reduction will reduce pain from the weight of your breast but it may not reduce the pain due to you monthly cycle because this hormonal.  It may help by removing enough of the glandular tissue that the pain is not as noticeable.  I would speak with a board certified plastic surgeon to help you through this decision.