I cannot answer whether or not these people could have made it to Europe, but the Pacific Northwestern Indians had some impressive boats. Some of the canoes they constructed were used for whaling which means they were advanced enough to make into deep enough water where whales can be hunted. Additionally they were used for warfare and could fit a large number of warriors. Heres one of these canoes that can be found at the New York Natural History Museum.

source: North American Indians, Alice B. Kehoe

On his fourth and final voyage to the New World, Christopher Columbus and his small flotilla of three ships encountered a very large canoe near the east coast of Honduras. This canoe was longer than Columbus' flag ship, but had no sails, a very narrow beam and the free board was to low for any trans-oceanic voyages. They could make the ninety mile trip from the Yucatan to Cuba and from there go to the Tanio people in Haiti. There is limited evidence that the Maya had some contact with the Tanio and taught them the ceremonial ball-game. However, the large canoes encountered by Columbus were primarily used on the trade route from the Veracruz area around the Yucatan peninsula to Honduras.
Off the west coast of South America, the initial voyage of the Pizzaro brothers, to Tumbez, Peru encountered a rather large balsa raft. This vessel was nearly as long as the Pizzaro's caravel, had a wider beam and had a sail, supported by an A-frame. These balsa wood rafts were used on the trade route from Panama to the north coast of Peru. Thor Heyerdal even thought they could make trips far out into the Pacific ocean, There is an oral tradition that Tupac Yupanci made one such trip, before becoming the Sapa Inka or supreme ruler of the Inka Empire. However, Thor Heyerdal's theory has fallen out of favor since it was first postulated in his 1948 book "The Kon Tiki Expedition: By Raft Across the South Seas". That book is also my source for both the large Mayan canoes and the balsa rafts on the west coast of South America.