Will a deceased Christian wife, who showed an inclination towards Islam and died before officially converting to it, be judged as a polytheist in the Hereafter, or is there a possibility that she will be judged as one who was on her way to embracing Islam?

The matter of the Hereafter belongs to Allah, and He is the Knower of the realities of affairs and the inner workings of souls. The mere fact that she was on her way to embracing Islam does not indicate that she died a Muslim. The original presumption remains that she died as a disbeliever, and consequently, it is not permissible to ask for mercy for her or seek forgiveness for her.