No.
It was precisely the Divine nature of Jesus which demanded a sinless Virgin. His Divinity is all holy and the source of all holiness. This Divine holiness can not, by its very nature, be countenanced by sin.
Mary was not Divine. She was human. The Church teaches that "through the centuries the Church has become ever more aware that Mary, "full of grace" through God, was redeemed from the moment of her conception." Mary's humanity required that she too, be redeemed.
Incidentally, in light of what I've said here and up-thread, I think it's worth pointing out how the Catholic teaching on the Immaculate Conception of Mary, (contrary to what Protestants usually say) actually exalts the person of Jesus because it emphasizes His purity, holiness and Divinity. Contrast this with the Protestant idea that "any womb would do". Tsk tsk!
Ironic, no? In fretting about Mary's singular privilege and worrying that it may be taking something away from Jesus, you actually diminish Jesus by insisting that any "house of sin" or womb could have nurtured him for nine months.
As I pointed out earlier, the "any womb would do" approach collapses when you consider how exacting God's requirements were for the first two Arks.
God is good!
"Seek and you will find" = He will answer with faith!
We have a supernatural God!
Praise Jesus and as the angel and the Holy Spirit said in scripture Hail Mary! That is it for real! Period!
Amen! Amen! Amen!