It was inevitable that the "native people" here would lose their dominance, no matter who had traversed the oceans, in any number, with intent to stay. The harsh reality was that various tribal groupings, based on neolithic hunter gatherer frameworks had neither sufficient manpower, nor technology to defend what they were holding from any outside group who possessed superior technology, and the concomitant increased manpower accompanying said technology.
Had the Black Death truly "depopulated" Europe, making it a veritable ghost continent, the colonizers of North America could have been Islamics, where the native people would have been faced with the stark choice, as stated earlier in the thread, of submit to Islam, and being Arabicized, or be exterminated. If it had come from the west, from China, well, the more recent model of Tibet gives us the inevitable outcome. In short, it did not matter who it was that 'discovered' them, the outcome would not have been any other than their displacement as the dominant culture.
The fact that it was a culture where Christian principles held some sway, even if only partially, allowed some remnants of the native cultures to survive...
the infowarrior
Excellent point concerning the result had Europe been depopulated.
a thoughtful reply, thank you.