Current opinion is that they almost certainly did. There are a few main lines of evidence for this. The strongest one is sweet potatoes. The sweet potato was first cultivated in either Central America or Northern South America roughly 5000 years ago. Yet it was also cultivated throughout polynesia before the Columbian Exchange. Additionally, the Maori word for sweet potato is "kumara" seems to be a borrowed word from the Quechuan "cumar" or "cumal" for sweet potato. On top of that, there is evidence that the bottle gourd (calabash) cultivated in polynesia may have come from the Americas as well. Another line of evidence is the current day population of Easter Island (Rapa Nui), whose genetics are strongly indicative of a lineage that includes indigenous South American ancestry going back to before the Columbian Exchange as well.

Are these lines of evidence bulletproof? Hardly. This is still an active area of ongoing research. But right now it looks like a reasonably strong circumstantial case.