The Commonwealth happened due to a dispute over one monarch for the two Kingdoms, which is why Scotland was involved in the English Civil War and why Cromwell invaded Scotland and also why Scotland joined the Commonwealth. All this would be butterflied away if the union of the crowns never happened.It did, between the Battle of Dunbar and the Restoration, so yes, but that's not the likeliest outcome.
Even just before 1707, a whole variety of solutions to the succession and commercial issues were floated on both sides of the Tweed. Not all of them involved state union.
The latest possible death date for an Artorius is 538 anyway, about 10 years before the plague of Justinian and the 6th century cold period wrecked the romano-british- the last bit is what you have to stop from happening to have a Britain with enough population and wealth to resist invasion and for the population to not leave as much as it did IOTL.
Until that point, anglosaxon presence is a bunch of saxon clans around the Thames, jutes in Wight and Kent and Angles in East Anglia and Lindsay and maybe "Deira" which at the time is a tiny fraction of Yorkshire.
All right.... so there's no way the Roman-Brit culture can hold out?