Well, i'm half 'Celt' (scottish, irish) and half english. Traditionally we English think of the Irish as having red hair. In any case, Celts are traditionally fair haired, not dark haired.
This is obviously a drastic over simplification. However I'd feel fairly confident in saying that a person who has dark brown hair and *especially* dark brown eyes, would not be considered typically 'Irish looking' or 'Celtic'.

Hmm btw who was the other 'English speaker in CIS' vote?