Weather eventrs are depressingly popular in Counterfactic history these days aren't they? Though the North Sea is pretty bad, it is quite plausible that a fleet could be lost that way.
IMO England will not gain anything from the victory. Anglicanism was a blip, historically speasking, and as a religious phenomenon it has no future in a Europe dominated by the Lutheric north and the Catholic centre. It is conceivable ATL, though, for England to follow Scotland and go Genevan. Provided, of course, that the Empire doesn't just come back.
That part is pretty plausible, actually. Everyone looks at sixteenth-century Europe and sees a colossus bestriding the world, but Turtledove's story for all its flaws captures the internal fissures amnd precarious finances of the Empire very well. A serious defeat may well lead to the project of conquering England being shelved indefinitely. That's how Charles II ultimately lost the Burgundian inheritance, after all.
Turtledove's presage of a great future is ridiculous, of course. Not that I can't see the psychology behind it - a maritime superpower, neither Catholic nor Lutheric, welcoming to Jews and devoted to science is a beautiful vision for someone whose family is only a few generations away from being servi domini. But seriously, England only has a future as a maritime power and that is all but impossible without access to the Indies. The best a non-Catholic England could hope for (and let's disregard the improbability of this 'Anglican' big-tent church for now) would be to become France's catspaw rather than an imperial outpost. It could have saved it the interminable Scottish wars, but at the cost of much of its maritime prosperity.