Why does it have to by "Senator of NY?" It's a bullshit parameter. No, I don't think she would necessarily have become Senator of NY if she were not First Lady. But she wouldn't have been a "lawyer from Arkansas" if she didn't marry Bill. She likely would have been a DC lawyer or a California lawyer.
I mean, in order to really engage the counterfactual you have to take Bill out of the picture. With Bill out of the picture, she never goes to Arkansas. Given her education and (limited) political work experience, I think it is quite safe to say she had quite a bright future in political office had she wished to pursue it.
Pretending her success is solely due to Bill is bullshit and you know her.