Kitty Pride wouldn't have physical strength enough to strangle Superman. However, she could reach into his chest cavity and close off the ventricles around his heart if she used all of her strength.
I've always thought Shadowcat's powers were simply an underdeveloped form of telekinesis. She can only phase her own body much in the same way Flash vibrates his molecules through solid matter. I've always figured she already has Phoenix-level capability, she just simply hasn't been properly trained.