At first, thinking about how the issue of Mary has been quite hard to get around in my own spiritual journey, I would have said yes, more Protestants would become Catholic.
But thinking about it, the answer is in fact no.
Because if all it takes is the veneration and intercession of Mary to drive Protestants away from the Church, then I highly doubt they would have entered the Church anyway.
Because, what convinced me of the truth is the role Tradition plays, and the beliefs of the early Christians. The belief that Jesus founded His Church upon the Rock, Peter, and that this Church would not be prevailed over by the gates of Hell.
The Magisterium and Sacred Tradition are just as fundamental as Sacred Scripture. If a Protestant can see and understand the truth of the Papacy, then I can assure you that Mary will not pose too much of a problem.
When one accepts that Christ established one Church, that would be built on Peter, the rest follows eventually. It might provide difficulty, but certainly not complete dissuasion.
Now, if the dogmas surrounding Mary were something unrooted in Tradition, then you might have a point. But they’re not.
At the end of the day, if a Protestant was ever considering Catholicism, Mary would not be the number one problem, and would not be a main stumbling block. The number one problem, you see, is the authority and infallibility of the Church. Once one gets their head around that, and understands the scriptural backing for it, then the other doctrines are easier to understand.
To conclude, the gift of the Mother of God to the Church far outweighs any impediment that may be caused to Protestants. And to reiterate, while it may cause difficulty, a Protestant who is seriously considering the claims of the Catholic Church will not be dissuaded merely by Mary. I mean, it really is meaningless for someone to say “Oh, I can accept the authority of the Church, and the Papacy, and Tradition, and purgatory, and the Eucharist… But Mary, y’know, that’s just a deal-breaker. I can kind of see why the Church is infallible and all, but Mary just ruins it for me.” Y’see the problem here? Mary is never going to be the deal-breaker. It’ll always be the authority and origins of the Church.
And if Mary wasn’t there, then the question would just be “Would more Protestants become Catholics if it were not for purgatory?” or “confession?” or “infant baptism?” or “papal infallibility?”
If a Protestant could accept those above things, then Mary isn’t going to dissuade them. Cause a lot of confusion, difficulty and strife, sure, but actually prevent them from entering the Church? No way.