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Yes. If he hadn't taken Obi-Wan with him at the beginning of the film (where Dooku pinned Obi-Wan under the slab), the Chancellor (Emperor) would have drawn him to the dark side much faster. The Emperor played on his emotions. I think that even if he had done nothing, she would have survived anyway.
Although...what if she had stayed alive? Wouldn't Anakin have been able to return to the light side of the Force again?