No. Keep working away at the opportunities as they arise, and keep networking. I am simply pointing out some of the realities.
You might well end up flying for BA, I have no idea. Whatever you do I wish you success. Where there is a will, there is often a way! Neither should set your sights or your ambitions any lower.
You have highlighted one of the many potential pitfalls along the career path, but that doesn't mean it is insurmountable.
Good luck.