No, because as soon as he dies, people will react against his radical Protestantism, just as they did after Cromwell in OTL (and were all merry and tolerant of high-churchies and Catholics for 20 years after the killjoy decade).
Well, how long are we supposing he lives? If Mary had ruled for a generation, her re-Catholicization might have stuck, no matter how unpopular the burnings. But if Edward lives, with a fairly long reign, there's no re-Catholicization effort at all, just a steady slide to the "left."
Also - just to be speculative here - what would a Presbyterian England really look like by, say, c. 1580, when in OTL the Catholic Church started really pushing back? Our image is compounded of the dour Puritans and the dour Scottish Kirk. But the Dutch Protestants, also Calvinists, developed a far more tolerant style.
I'd argue that there may be very deep roots of semipelagianism in English religious life, and rigorism just doesn't go over, no matter what the official theology. An Edwardian church would probably develop a moderate wing, and Edward himself might moderate as he grew up and discovered wine, women, and song - hey, as dad said, it's good to be king. As Leej kind of hinted, we tend to view Edward in light of knowing that he died at 16, so "small, sickly boy" just comes to mind, and we spin a whole image of a wheezing, pale little religious fanatic.
But to my broader suggestion, sauce for the goose, sauce for the gander. There is a stereotype that a Catholic restoration in England will look like Spain, and end up in a backwards world like Kingsley Amis'
Alteration. But perhaps English Catholicism would end up with a flavor like high church Anglicanism. Not like OTL Anglo-Catholicism, because it would be the mainstream, not a minority movement.