Not necessarily. They only said "Cf.", meaning "compare". The Shorter OED says "origin unknown" and "Anglo-Irish". The definition is "A lively tune in triplets for harp, fiddle, etc., slower than a jig; a dance to this." So the differences are that the good folks at Oxford think planxties are lively, not mournful, and they don't mention any Welsh connection. Are there Welsh planxties? Are there mournful ones?