Conversion is a work of God. He knew us even before the foundation of the world, the date of our birth, our childhood, the difficulties that we will have in life, the day of our conversion, and how He will do it. He is the author and finisher of our faith.
We may consider conversion as a moment in our lives and our final salvation as on-going, though the Lord had declared that none of the elect shall eventually fall.
The big failures that we will have, he knew it. Though we may suffer the earthly consequences of our sins, our salvation goes-on by His grace. In the interim we are undergoing sanctification, that all true believers will radiate Christ our Lord, and His will in our lives.
There are indeed false conversions, but no one has been given a mandate to effect conversion which is the work of God alone. However, the preaching of the gospel, preaching about sin, about the judgement to come must continue for
faith comes by hearing the word of God. To preach, baptize, and make disciples of all nations.
Going back to the 'sinner's prayer', it is only God who can
decide, if He will save one, so be it. His hands are not tied-up with our theological understanding or doctrinal sentiments. Or, if He will use it as a preceding event as
He works out our salvation.
But we can fully trust in His words that whosoever believes in Him will not perish and that His grace is sufficient for our weaknesses as we continue to the path of humility and faith in Him, in blessings and sufferings.
His offer of salvation is sincere. The gospel can be simple enough and so encompassing for He knows how deprave we are, that all of us will perish unless He extend His grace.
If you will have unction to offer sinner's prayer, so be it in humility before God, but be very careful about it