It is very easy to misinterpret data given by mammograms, and this is a reason so many benign growths are treated so aggressively. Of course, when you treat small growths aggressively, then you end up preventing later stages of the same disease, so by definition it would be effective at doing that job.
Mammograms are effective in the fight against breast cancer. Though this technique may not catch all early stages, it is one we must not do without. If only a few women are tested this way and cause a discovery of an early growth, we must consider it effective for all.
This seems to go without saying, that any measure that helps to detect cancer in its early stages would be effective at preventing late stage breast cancer. Cancer can remain undetected for some time because there rarely are any symptoms early on. It's also not something that one thinks about that often. Having routine mammograms scheduled is a way of bringing it to your attention periodically, so if you have early stage cancer it can be detected before it gets serious.
Mammograms are a diagnostic tool. They are not meant to prevent breast cancer, they are meant to detect it early enough to allow for treatment. However, they can prevent cancer from becoming late stage, by detecting it early enough that's it's eradicated before it has the chance to become late stage.