[Angry Hill Troll]

Possible outcomes of Galadriel as well as other potential claimants using the Ring are also discussed in this thread. As you will see there are different opinions expressed. Kuruharan points out that Tolkien says in one of his Letters that only Gandalf could have actually claimed the Ring for himself (even so, it would have corrupted him). Also, he points out that one must be careful in quoting something a particular character says, since Tolkien might not have conceived of that character possessing a complete and accurate knowledge of the situation.

In spite of the statement in the Letters, I still see the situation with Galadriel as somewhat complicated. In the introduction to (the several conflicting accounts of) "The History of Galadriel and Celeborn" in the Unfinished Tales, Christopher Tolkien states that

There is no part of the History of Middle-earth more full of problems than the history of Galadriel and Celeborn...the role and importance of Galadriel only emerged slowly, and...her story underwent continual refashionings.

In what Christopher Tolkien describes as "a very late essay" about Galadriel, the following statement is made:

It was not until two long ages more had passed, when at last all that she had desired in her youth came to her hand, the Ring of Power and the dominion of Middle-earth of which she had dreamed, that her wisdom was full grown and she rejected it,...

The wording of this last sentence makes it sound like Galadriel could have successfully claimed the Ring for herself. Otherwise the dominion of Middle-earth didn't come to her hand, only a false promise of it did. It's possible that this question is one of the things regarding Galadriel about which Tolkien changed his mind.