It was the same Kyuubi then in the Madara v. The First battle? How did the First manage to defeat both Madara AND the Kyuubi if this was the case?
We were never given the exact details.
If the Sharingan was supposed to be derived from the Byakugan, shouldn't the Byakugan have all the same evolutionary potential of the Sharingan? Whenever those eyes seem to upgrade they increase logarithmically in power. Byakugan should be able to do the same.
I don't think so if for example the Byagukan evolved from the Sharingan than it shouldn't necessarily have all the same abilities as the Sharingan considering that most things that go through evolution sometimes lose certain features they once had in the previous stage(s) but in turn might receive some beneficial enhancements.
Another version of the answer
No because people would grow to dislike the Byakugan just as much as they hate the Sharingan.