Not at all. But one has to assume that everything they believed about Jesus was really true, right?
You would then need a different way of knowing that the Bible is true, though, and that all these other things are not true.
If we say, how we know that the Bible is true is that the Pope made an infallible declaration based on the findings of the Council of Carthage, who examined the Holy Tradition and found it to be so, then what you are saying is that how we know it’s true, is that the Pope is infallible, first, and that the Councils are reliable.
But, if you say that the Pope cannot be infallible, and Councils are sometimes unreliable, then you have to have a third criteria, to show that although the Council of Ephesus was wrong about Mary, the Council of Carthage had to be right about the Bible, and that although Pope Pius was wrong about Mary and was wrong to make an infallible declaration based on the findings of the Council of Ephesus with regard to what the Holy Tradition says about Mary, Pope Innocent I was right about the Bible, and the Council of Carthage proves it because of what the Holy Tradition gives us with regard to the Scriptures.
Where is your third criteria?
What makes the difference between an infallible proclamation based on the findings of the Council of Ephesus, and an infallible proclamation based on the findings of the Council of Cartthage?