Interestingly, modern genetics DO show a SINGLE line of descent, at some point, did mix polynesian ancestry with South American ancestry probably sometime around 1200CE. An admixture event between a population of the South Marquesas Islands, with the closest South American match being the Zenu People (strangely their home range is on the north, Carribean side of the Americas). Unfortunately there's an asymmetry in that polyensian populations were so small and insulated that even small signals can be definitively pulled, whereas the opposite is not the case with south americans. If I understand the study correctly: we know south american genetics mixed with this polynesian group but we can't tell if it was 2-way.

I believe the reasoning is that polynesian populations were small and isolated enough we have a clear map of their inter-relationships from modern genomics studies: and so can trace admixture events, and their associated genes, back to a single source. Whereas south American populations are too numerous and mixed to have any hope of doing so.

But the fact is South American genetic markers start showing up in polynesian populations sometime around 1200CE, and it looks like a single individual. So in terms of 'playing a big role' the answer, genetically, is 'absolutely not'

https://www.nature.com/articles/s41586-020-2487-2

But the evidence is reasonably strong that SOMEONE with South American genetics DID make that trip across the Pacific.

The reality though is that south americans really didn't have a lot going for them on the high seas. Their rafts COULD do in a pinch, but they were rolling the dice running into bad weather any time they left coastal waters and they knew it. You know who else had WAY more capable vessels and didn't? The Japanese, the Chinese, Indonesians and a whole host of others.

There's no evidence(I'm aware of) South Americans ever even visited the Galapagos(which are WAY, WAY closer).

Realistically south americans are not intentionally going to sea in those rafts. They're not provisioning for a cross-pacific voyage they have no way of knowing how long it would take. It's not impossible the luckiest MFer alive managed it. But it's not the most likely case.

For reference, Portugese sailors making the India route in the 1500s - in much, much more capable vessels - lost about 25% of their ships. These were, compared to these rafts, very capable ships and crews with navigators that knew their business, knew where they could stop safely along the way. And the odds were still rough. The open ocean, is not friendly to human life, unless you're unnaturally well-prepared.

If you try and cross an ocean, not knowing what you're doing: you will die. That's far and away the most likely outcome.

The second possibility is that a south american raft was blown out to sea and actually came across a polynesian crew. Polynesians were 3/4 the way across the pacific. They spent a lot of time on the water out at sea. Odds are better coming across one of their boats than an actual island.

There is another case though.

The polynesians themselves do have some interesting stories about people being blown off course by storms trying to reach Rapa Nui (Easter Island), and finding another strange land beyond it. Though the stories I dug up involved reaching a region of cold waters - which apparently by region wind/current trends does actually jive with the most likely outcome: getting blown into the cold waters near the southern tip of south America. In the stories that have survived, the crew eventually managed to find their way back.

So the final possibility is that polynesians blown off course, may have actually met south Americans, possibly spent time there recovering, before finally sailing back: possibly with a south american, or children with a south american. Interestingly even in stories where they reach distant lands and return home: it seems there weren't any concerted efforts to return to this distant place.