If a woman doesn't have fully developed breasts, is it still possible for her to get breast cancer?

Yes: If by fully developed you mean size, that does not have bearing on breast cancer.

Yes: By not having fully developed breasts, do you mean, pre-pubertal? Or do you mean smaller breasts? Breast cancer is dependent on many factors, many of which we know, and may of which we don't. Yes, it is possible in smaller breasted women, and is also possible in men.