What would have happened if Galadriel took the One Ring?

[Iarhen]

As Tolkien says in the book, only the ones that hag big power of their own, and a trained will in the command of others, could successfully use the ring for their own purposes.

In this case, Galadriel had enough power. Not only the one that came from Nenya, but her own as a Noldorian, from the royal house, and oldest among the Eldar. And she had enough will and mental power to see what Sauron thought and to, with her mental abilities, keep Lorien as a safe place.

So, what would have happened if she took the ring? Would the ring betray her and lead her to her fall, in favour of Sauron? Or would the ring become truly hers and in time, would she take the place of Sauron as the Dark Lord (or Queen???)? If she had taken the ring when Frodo offered it to her, would she had enough power to destroy Sauron & Mordor?

Thanks for the answers...