I believe that Orson Scott Card has actually explored this idea in his book Pastwatch: The Redemption of Christopher Columbus. You might want to look into that.
As for my opinion on this scenario...well, that's highly unlikely even with PODs that advance Native American civilizations, (which would have to be agricultural ones, alternate plant and animal domesticates that allow the Native civilizations to develop faster). The Americas were smaller than Eurasia, which would mean a generally smaller population. This means less societies to develop new ideas, less innovators to advance technology. So even if Native Americans began practicing agriculture as early as Europeans and Asians, it would be unlikely that their technology would advance further fast enough so that they could discover Eurasia first.
Assuming it did happen? At very least, great upheaval and change for both sides of the Atlantic (or Pacific). Possibly less bloody than OTL, but there is nothing to indicate that these Alt-Indian explorers would be any kinder than European explorers.