Funnily enough, I was just reading about Canute not five minutes ago.
My takeaway from the whole situation is that there's no way Canute would have invaded without a modicum of security on his southern border. If Rudolf of Rheinfelden were to survive the Battle of Elster and continue to pressure the Emperor whilst other anti-kings rose as per OTL, this would likely occupy Henry's attention and perhaps even lose him the throne (which is a whole 'nother mess of divergences I won't get into). As a result, Canute is free to invade England.
With all that being said, does he win? We can't say, of course, but as others here have mentioned, the Bastard had already prepared an army to deal with him. Moreover, despite my personal hatred of the man, I must admit that William was a seasoned and accomplished commander with talented subordinates. Canute is largely unproven historically. For all we know, he could have been the next Alexander, but probably not.
The most likely outcome is a Danish defeat. However, this is a tragically boring ending to a potentially fascinating POD, so let us presume that Canute proves talented and drives l'Batard back to Norman shores. The Danes have proven that their Frenchified cousins are no match for Scandinavian steel and opened a new verse in the Knútsdrápa. All is well and good in those lands lapped by the Northsea.
Or at least, it seems that way until our sainted protagonist actually bothers to look at the state of his new realm. England in 1084 is a mess from the perspective of the Danes. The Harrying of the North was only 14 years ago, and the Domesday Book, IOTL compiled in 1086, makes it clear that northern England was both heavily depopulated and impoverished from the dread deed. Southern England, while rapidly getting to its feet, has also suffered a series of revolts and reprisals in the last two decades which have left many fields fallow. Worse still, the indigenous Anglo-Saxon and -Danish nobility has been gutted. In its stead are Norman and, in some cases, Breton lords loyal to William, who are outnumbered and often at odds with their supposed vassals. To pacify his new realm, Canute will have to deal with this nobility of pillagers (whether through carrot or stick), a southern population unhappy with yet another foreign king, and a devastated northern England.
I would figure he follows a similar path to William himself, if he's smart, and strips the titles of the nouveau riche en masse, replacing them with his own supporters (and naturally direct rule in some cases). Do his heirs (likely one of his MANY brothers) keep England? Given the legacy of Danish rulers in fair Albion, I tend to doubt it. But if the land is successfully pacified and the Anglo-Norman nobility driven out, there's certainly a chance.