So the question originally posed was “Can Mary convince God to save someone who doesn’t deserve it?”
I would answer no, for a whole host of reasons.
The first thing that I would address is the premise in the question that a person deserves salvation. The very nature of salvation is that it is unmerited by the beneficiary. As the apostle Paul tells us:
“For we have already charged that all, both Jews and Greeks, are under sin, as it is written: None is righteous, no, not one; no one understands; no one seeks for God. All have turned aside; together they have become worthless; no one does good, not even one.”
So in that sense, grace and by extension salvation, is wholly unmerited by all. Paul makes very clear that justification is by grace through faith, not by works or merit. “For all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith.”
The next thing we should address is whether intervention is needed in order to precipitate God’s grace. The answer is no. All throughout the Bible we find that God’s redemptive plan was already manifest long before Mary. We see that in God’s promise to Abraham, that through his offspring all nations would be blessed, this continues with the Mosaic prophesy that one would arise after him, and see this continue through the prophets, especially in Isaiah where the coming of the Messiah and his work was already pre-ordained by God.
Finally, Paul sums this up for us in Ephesians: “For by grace you have been saved through faith. And this not of your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.”
God does not need to be convinced or persuaded to enact his redemptive plan, it was prepared beforehand.
Next, it is not Mary who is our intercessor, but Jesus. As Peter proclaims in Acts: “And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.”
Hebrews makes this clear that Jesus is the high priest who makes intercession for us. Jesus is the high priest and mediator of the new covenant in his blood. “Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people.”
Not only is he the sole person to provide the atonement for our sins, but he is the perfect mediator, not needing someone to intercede on someone’s behalf, but perfectly able to understand and meet our need for redemption. “For because he himself suffered when he was tempted, he is able to help those who are being tempted…For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin. Let us then with confidence draw near to the throne of grace, that we may receive mercy and find grace to help in time of need.”
Lastly, we have to remember that Mary herself was the object of God’s grace and mercy. As Mary herself says, “My soul magnifies the Lord, and my spirit rejoices in God my Savior.”