Will fibrocystic breast disease eventually or inevitably lead to breast cancer?

NO. Fibrocystic disease is now termed fibrocystic change and by itself is not associated with increased risk for breast cancer. However, regular breast self examinations and mammograms are still recommended.
Its not a "disease" The term fibrocystic "disease" is outdated and inaccurate. Fibrocystic changes are very common (can be found in just about any women's breast tissue), are benign, and do not increase breast cancer risk. Increased breast density (a subjective mammographic finding) is associated with increased risk. Findings of atypia along with fibrocystic changes on a biopsy are also a marker of increased risk.
No. There is some evidence that "dense breasts" are at increased risk for developing breast cancer. Breast cancer may be less detectable in breasts with fibrocystic changes. However, the presence of fibrocystic change does not lead to breast cancer.
No. Fibrocystic breast disease will not eventually become breast cancer. Besides the pain and discomfort associated with fibrocystic breasts, cancer screening imaging is not as effective in these denser breasts and so careful and regular examination is wise.
No. Women with fibrocystic breast disease will not "inevitably" have breast cancer, although fibrous breasts does make it more difficult to do self breast exams and may make it slightly more difficult to diagnosis breast cancer via mammograms. All the more reason to do monthly self breast exams and yearly mammograms in age-appropriate women.