The simple answer is no.
Partly this is due to a calendar change. The date of the storm, on the day of the storm, was the early hours of March 11. But due to an eleven-day shift in the calendar in 1752, the successive anniversary Newton celebrated for the remainder of his life was the recalibrated date of March 21, 1748. This stands as the most accurate date.
More importantly — and contrary to most popular myth of Newton’s remarkable life — the shipwreck does not mark his conversion, but what he would later call his “great day of turning.” The near death experience at sea, and God’s “deliverance” of his physical life, so deeply startled young Newton from his life of moral debauchery that it sent him earnestly searching for God’s grace in the gospel (even to a church in Charleston, SC that still stands today). But that process had only started.
In my research into his life and letters, the best guess I can render is that Newton was converted to Christ 18 months after surviving the storm at sea, and I base this on his 1795 letter, written as an old man recounting the key dates in his life to a friend.
I cite the letter in Newton on the Christian Life, page 35:
I have still some faint remembrance of my pious mother, and the care she took of my education, and the impression it made upon me when I was a child, for she died when I was in my seventh year. I had even then frequent intervals of serious thoughts. But evil and folly were bound up in my heart; my repeated wanderings from the good way became wider and wider; I increased in wickedness as in years: But you have my Narrative, and I need not tell you how vile and how miserable I was, and how presumptuously I sat in the chair of the scorner, before I was twenty years old. My deliverance from Africa , and afterwards from sinking in the ocean , were almost miraculous; but about the year 1749 (I cannot exactly fix the date) the Lord, to whom all things are possible, began to soften my obdurate heart. (Letters [Taylor], 125).
The rest, as they say, is history.