There are Irish Kennedys and there are Scottish kennedys. Totally different families. If it’s appalachia, it’s likely Scottish.
CC
I’ve known Canadas and Cannadys, just enough to know that it’s a cognate of Kennedy. There are actual Irish who settled here (one great grandmother of mine was a Neal originally O’Neal for instance) but they’re far outnumbered by Scotch-Irish, so you’re likely correct. Canadas or Cannadys tend to be more Cherokee than most, too.