I don't believe the Catholic Church teaches any different in that regard; in fact Mary's free will is a very important part of Catholic mariology. It is a misunderstanding of the doctrine of Immaculate Conception to say that Mary was incapable of sinning. Right, Jo?
That is an interesting question. I am not sure if the infallibly pronounced doctrine of the Immaculate Conception covers the speculation that she COULD have sinned. I do know that she was born without concupiscence, thus, she was not subject to the temptations of the intellect or the will. She could have been tempted from without (as Christ was by Satan and the Pharisees), but not from a wounded intellect or will.
Whether she could have succumbed to an external temptation - such as a temptation to doubt God's plan while watching her Son hang from the Cross - I am not sure how or if the Church has defined it. Without concupiscence, which was bound within her, as opposed to removed (as in Christ's case), I would find it hard to believe that she COULD have sinned. I personally would say "no".
Mary's fiat is important, but I am not sure that this applies to remaining sinless, but rather, her "yes" in the face of not knowing God's plan and trusting in Him anyway (as opposed to Zechariah).
Let me know if you find out for sure.
Brother in Christ