Sorry, I think I had misunderstood your original question to be asking about the ancient origins of the Celts rather than whether or not they spread anywhere Eastern. Yeah, they did spread East, a little. Turks have a tiny amount of Celtic Y-DNA IIRC. But the great majority of Turkish R1b is Anatolian, not Celtic.
Defining Celtic may not be so hard, try this: the languages and culture associated with known P-Celtic and Q-Celtic language speakers, which are known to be closely related, and the ancestors that they share, not in common with non-Celts. That should exclude Romance language and culture and probably also Lusitanian (barely). But it keeps everything you think of as Celtic: Irish, Welsh, Gaulish, Celtiberian, La Tene, etc...