Seems somewhat likely to have overlap, just takes one set of second cousins (or closer) getting frisky.
But even though I can trace my surname direct ancestors back to the early 1700 in the US, within 8 generations my family tree (that I can reliably track) spreads to a dozen different countries. And a DNA test let me know that despite being almost entirely English/Scottish/Irish they have people with enough DNA matching in their database to count as a 3rd cousins or parents 2nd cousin in random places all over the world.