Well the reason they were able to put up such resistance OTL was because they had plenty of time to recover from the Eurasian diseases and adapt, the Fusangese took quite some time to expand beyond the Beautiful Mountains (The Rocky Mountains).Are you sure about that? The east had some of the most powerful native states (the Iroquois and Powhatan confederacies) that put up the toughest fights against the Fusangese, while the tribes around the initial settlements on the west coast were just hunter-gatherers. I think your "United British" may be in for a tough time if they try to land...
If the United Britons arrive early enough they could easily take advantage of the Iroquois and Powhatan Confederacies before they had time to recover. But I mean, even if they did, they don't have the population of East Asia, I don't see how they could colonize the way fore example the Chinese did.
Plus would they even go there? From what I heard the Europeans at the time thought the Earth was flat (no joke), they thought they would fall of the planet if they went too far West. I don't know how true that is tho.
What was European shipbuilding like at the time tho? Have seen some pretty interesting pictures of some European designed ships from the time, they look a bit odd, but how seaworthy were they? I know the Vikings had good ships.