Had the EU existed then, he'd have never had the chance. Given current EU red tape, efforts to make a replica of La Mora, the ship Williams used to become The Conqueror, mean it may still not be ready for the 1,000 year anniversary. Unless Great Britain, having shucked off their two-decade experiment in the EU, build it for them.
The place that decreed that water would not cure thirst is saying La Mora II is a yacht and so won't be allowed to sail unless it meets modern EU Maritime Affairs regulations. It's supposed to be long and thin, as memorialized in the even longer Bayeux tapestry, but the EU says a boat a hundred feet long and only 15 feet wide isn't seaworthy.
Bayeux Tapestry. Scene 38, public domain from the website of Ulrich Harsh
Saying a boat that crossed the English channel to successfully take over England couldn't have done it isn't as stupid as Galileo declaring the moon had no impact on tides, and those only happened once a day, but it is close. You'd think the EU, smarting for losing $12 billion a year that England can now spend at home, would want a reminder about how they took over the place in the past, but the group behind the project says red tape will mean another 5 years before they'll even know if they can put an oar in the water.
(1) Harald Hardrada, King of Norway, and Harald's brother Tostig were also not buying claims of a deathbed bequeathal by King Edward and intended to press their claim. William benefited by arriving last when the Anglo-Saxon army was weakened.