Here's a quote I dug up from Nebulus.org.
Likewise, scholars say they have laid to rest the notion, made popular in
the 1950's by the Norwegian explorer Thor Heyerdahl, that the original
people were Indians from South America. He thought he saw similarities
between Pre-Columbian Peruvian and Easter Island architecture. To make his
point that such contact was possible, he sailed westward from Peru in a reed
raft named the Kon-Tiki.
Linguistic, cultural and genetic evidence, most anthropologists agree, shows
that the people of Rapa Nui were Polynesians. Their language is Polynesian,
though it has changed so radically as to indicate an early separation from
the home culture and centuries of isolation. The few surviving examples of
ancient writing are in a script that has yet to be deciphered. The statues
and other artifacts bear a Polynesian imprint, and in 1994, the DNA from 12
Easter Island skeletons was found to be Polynesian.
THE SETTLERS Polynesians Found Isle Next to Nowhere
The first settlers apparently arrived from the west by canoe sometime
between A.D. 400 and 750. This was a time of epic voyages of Pacific
settlement. The migrating Polynesians, originally from Southeast Asia, had
reached Tahiti and the Marquesas islands by 300 before going on to discover
and occupy Hawaii and New Zealand.
OK, my geography could be faulty, but I believe that sailing westward from Peru would be mighty tough going.
Actually, it wasn't a reed raft at all. Was made of balsa logs. I guess you could call the Ra's reed boats, though. Details here:
As for the theory, it doesn't seem to be more than that the journey would have been possible.
Where do the recently (within the last two years) discovered Celtic structures in New Zealand fit into this picture?
There is no connecting proto language. Perhaps dumbassian, then again, maybe not.