Yes. The Catholic Emancipation Act 1829 makes it clear that the Prime Minister is entitled to be a Catholic. The last office to be specifically excluded was that of Lord Chancellor, but, as far as I am aware, the provision was amended in the late 1970s.
The one thing that a Catholic Prime Minister cannot do is make or advise on appointments in the Church of England. That is specifically listed as a felony.
The point is that times have changed, and the Bill has come forward. If there were to be no change in our plans for the succession, I would not be the one charging the barricades and saying that we ought to be changing them, but the Government have proposed this change, which they wish to limit to a very narrow sphere. They wish to limit it to making primogeniture equal among males and females, and to allowing marriage to Catholics, without considering the grating unfairness that currently exists in our laws of succession in an age of much greater toleration, and in an age in which so many of the areas in which the Queen is sovereign do not have an established Church.