When my family arrived in South Carolina in 1767, the record called those arriving on the same ship, "poor Irish Protestants", which was what the colony was looking for and paid for. They weren't indentured, their passage was paid, they were granted land in the far interior of South Carolina (near the Cherokee), and each given a quite reasonable money grubstake. For the next two generations they married other families of Scottish descent and moved west rapidly. My own family was in Missouri by 1806. Although my direct family did not intermarry with Native Americans, this did occur and one finds Scottish names among the Cherokee today.

So this small bit of evidence backs up what others have said, only I think the people may have been called Irish Protestants at the time rather than Irish Presbyterians. This is similar to the Church Affiliation Census in Ireland in 1766, where families were recorded as Catholic, Protestant, or Dissenters (the term Presbyterian did not seem to be used). In my own family's case, there is no evidence that they were ever Presbyterian; Episcopalian or perhaps Methodist seems more likely.