Listen to klezmer music if you want to hear the clarinet in a folk tradition. I can't remember most of the names offhand and don't have a link for you, but if you do a search on Andy Statman or Klezmer +clarinet that should get you started. No, it's not celtic, but there was a Jewish Lord Mayor of Dublin not too long ago, and of course there's Leopold Bloom. And on your original question, if you're a good clarinetist and you like Celtic music, then do it. Since the clarinet is probably the closest wind instrument to the timbre of the human voice, you might do something wonderful with the slow airs and sean nos tunes. You might even start a new tradition!

Aloha,
Mark