I've been using WikiTree to explore my ancestors. I see a Mary Paine Slocum (Paine-46) and a Mary Paine Tripp (Paine-49). The grandson of Mary Slocum married the great-great-granddaughter of Mary Tripp. Both Marys lived in Rhode Island. I followed ancestor trees of both back as far as I can. Mary Slocum's family came from Suffolk, England. Mary Tripp's family came from Lincolnshire, England and before that Suffolk. But I don't see a common ancestor.
I tried running a connection and it found the one through their descendants, the one I knew about.
This is an intriguing question, though I'm aware there may not be data to show a link. I ask it partly because I've seen those Rhode Island folks tended to intermarry a lot (I've already found a marriage of second cousins in the Slocum line).