All the promises of power the Ring offers, are lies. No one safe Sauron can bend the Ring to its will, and the spirit of anyone who tries would get destroyed and overwhelmed by the malice (and part of the consciousness) of Sauron inside the Ring, and either become a slave of the Ring, or a replica of Sauron. As Galadriel was powerful and wise among the Eldar, I believe she would not become a slave, but a replica.
Even though, I do not believe that "dark queen" Galadriel would be able to defeat Sauron, even with the Ring. Even with the Ring, Sauron and his armies still outnumbered the Free Peoples of the West. Even without the Ring, Sauron was still the most powerful being in Middle-earth and unchallenged until the arrival of Gandalf the White.
But as this thread is supposed to be fictional : she'd become a tyrannic ruler over the Free Peoples of Middle-earth, and either destroy all of Sauron's minions or keep them as slaves, at least until the Second Host of the West would come to have a chat with her.
Give up the Halfring, she-elf...