Marianna suggests: I keep thinking that the /k/ pronunciation of Celtic must be of the same nature as the /k/ pronunciation of the word ceilidh

The Gaelic (whether Irish or Scots) c is always a hard, /k/ sound, regardless of the following sound. I don't think there is any connection between the word céilidh (I believe the Irish is céili without the dh and I'm not sure about the é in the Irish) and the word Celtic. I don't doubt that there was some connection between the Greek keltoi and the Celts name for themselves. The Scots Gaidhealach is just too close and probably the dh was pronounced time back way back.