If William didn't contract a sickness and die right after landing in Britain, he could pull it off. Harold Godwinson's army was not in the best of shape after defeating Haldrada at Stamford Bridge-the Normans might put up a better resistance.
That said, I think having all that territory is not impossible, but really implausible. The French aren't that weak, and I don't see why the Normans would be able to conquer all of the British Isles. Do you know what year that map is from in this AH?
I heard roughly a century after Hastings.