This kind of argumentation is not unlike the mindset of many today who support what is today known as Pragmatic Evangelism. The notion is that the methodology of evangelism is irrelevant if the consequences are that people are saved. Some will respond to criticism of a minister or a particular methodology with "Well I was saved by the preaching of x," or "Well God saved me by y." It is the "ends justifies the means" mindset that has seeped into many churches today. As such, I believe Edwards's own response to this mindset, some 250-years ago, is still relevant even today.
Though we are to eye the providence of God, and not disregard his works, yet to interpret them to a sense, or apply them to a use inconsistent with the scope of the word of God, is a misconstruction and misapplication of them. God has not given us his providence, but his word to be our governing rule. God is sovereign in his dispensations of providence; he bestowed the blessing on Jacob, even when he had a lie in his mouth; he was pleased to met with Solomon, and make known himself to him, and bless him in an extraordinary manner, while he was worshiping in an high place; he met with Saul, when in a course of violent opposition to him, and out of the way of his duty to the highest degree, going to Damascus to persecute Christ; and even then bestowed the greatest blessing upon him, that perhaps ever was bestowed on a mere man. The conduct of divine providence, with its reasons, is too little understood by us to be improved as our rule. "God has his way in the sea, his path in the mighty waters, and his footsteps are not known: And he gives none account of any of his matters." But God has given us his word, to this very end, that it might be our rule; and therefore has fitted it to be so; has so ordered it that it may be understood by us. And strictly speaking this is our only rule. If we join any thing else to it, as making it out rule, we do that which we have no warrant for, yea, that which God himself has forbidden. [Humble Inquiry Concerning the Qualifications for Membership in the Visible Church]