No, Catholics reject the heresy of Calvin's TULIP. Everyone, including Mary, has/had full freewill. Mary freely chose to become the Theotokos.
You are undermining the Protestant position on Mary's sinlessness. If she had no freewill, she was no more capable of sin than the beasts of the field. Either way, Protestantism is undermined.
Peace be with you
You will say to me then, “Why does He still find fault? For who has resisted His will?”
But indeed, O man, who are you to reply against God? Will the thing formed say to him who formed it, “Why have you made me like this?”
Does not the potter have power over the clay, from the same lump to make one vessel for honor and another for dishonor?
What if God, wanting to show His wrath and to make His power known, endured with much longsuffering the vessels of wrath prepared for destruction,
and that He might make known the riches of His glory on the vessels of mercy, which He had prepared beforehand for glory,
-- Romans 9:19-23...just as He chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love,
having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will...
-- Ephesians 1:4-5
You give only TWO choices?
How nice.