Well, if Harald defeats Harold at Stamford Brige, you may have the most possible Norman/Danish alliance ending with a separation of England, in North/South lines, each side taking royal title.
Of course, it's extremly likely that tensions between them would eventually arise, at the benefit of the formers.
See, "North Sea Empire" was far from being an unified body, or even a "confederated" entity : each nobility and elite had its own interets and culture, and the royal hegemon wasn't popular even in Scandinavia.
Basically, every part of it regularly rebelled, forcing the king to take ressources to crush it, that in turn make nobles of other regions rebelling.
Giving that scandinavian succession was a bit particular (long story short, succession of titles was less a matter of dynastic succession than kingship succession : if your predecessor was both king of Danemark and England, even if you weren't related to him and elected in Danemark, you still had a legit claim on England), you'd have much room for infighting.
I could see a royal hegemon over several scandinavian titles, but not lasting too much on England (too far, and with a too distinct political identity) or even in Scandinavia at all (short of a PoD making Danish kings more powerful, and ruling over a more unified entity earlier than IOTL, and even that wouldn't be a magic formula).
Normans, ruling over a wealthy and relativly unified duchy, beneficied from proximity and more ressources/strategical focus.
A Danish victory isn't to be ruled out, but even there, you won't get rid of the huge division of the so-called "North Sea Empire". Maybe a danish dynasty over England, while not ruling over Danemark?