As ebarnacle says, the Basques financed a very profitable society for centuries by fishing the Grand Banks. So it certainly was possible to sail both over to Newfoundland and back. There's no reason why the Americans couldn't have done so. There may even be folk memory of it, though this would no doubt be dissed just as much as the folk memory (and early accounts) of Brendan of the Voyages now are by some.

As DNA testing becomes more widespread, and DNA dating more accurate it'll be interesting to see if pre-columbian nortamericano and sudamericano DNA turns up along the west coast of Europe and the east coast of Russia, China, etc.