Sorry, not
would but
could
What he said.
Over a thousand years a lot might change. Or very little.
The only almost certain thing is that there would be no Aztecs, with some other polities replacing them. Nom, nom, nom ...
Same with Incas. A week is a long time in politics. A thousand years? Mind boggling
The Americas could just as well still be in a wheel-less stone age, or in the bronze age, or even in the iron age.
Maybe even be trading with the Old World on their own ships. Or c.1000 establishing trade factories on European shores and buying slaves.
Still, contact with the Old World means diseases and a civilisational collapse due to population loss and severnce of trade ties..