Useful resources, yes. And I would encourage women in the UK to take part. But don't get your hopes up, unless they end up enrolling women at very high risk of breast cancer already, the number of women in the survey actually deloping breast cancer over the first five years will be very small, and so it will not be able to answer any questions.
These are called cohort studies. Once a predetermined number of women in the group have developed the condition of interest (breast cancer) an intense mathematical examination of all of their characteristics at enrollment takes place. The aim is to see which things are different in the group who develop breast cancer from the rest. Often an increased risk of 100% (twice as high) is considered convincing.
Many of the factors that will turn up, will be well known, such as age, number of children and family history. There will then be an effort to sift out less well known factors that may be playing a part in addition.
The problem with bras is that the number of women who do not wear bras (and that really means never) is so small it will be difficult to see any effect. As other posters have pointed out, it is likely that braless women are not typical (they are smarter), so all the other factors that make them different would need to be taken into account.
However knowledge is power.