No, I know of no connections between these families. But one of my ancestors, John Swarens(Swerin or Swern or Swerns or Severn or Severns or Severin or Severing or Severings or Swearingor Swearings or Swearins etc.) appears to have co-migrated with Christopher Brunk's family. John married Nancy Brunk. The Brunk descendency doesn't seem to know anything about her, but they have a few boys about whom nothing more is known than that they were born, so we are guessing she might have been the widow of one of them.
Christopher Brunk bought & sold land in Greenville Co. SC, as did John Swarens. So I'm looking at the other locations of Brunk land transactions for additional migration clues.
I'd be curious to know title of the book from which you got the abstracted records.