Yes and yes. I think it's kind of cheating though. My birth was a planned c-section and the doctor gave my mom a choice of days. She picked St. Patrick's Day for obvious reasons.
And, yes, I'm Irish. My mom is 100% Polish. I'm told my father is Irish and half Scottish. I have yet to identify where the Scottish roots come from. My Irish family Americanized their surname when they moved to the US, but the name originally started with O'... Can't get more Irish than that. But, my ancestors are "black Irish."
I don't know if you've ever seen a picture of me or not. Element caught my Polish cheekbones, eyes, and nose, so he tends to think of me as being Polish. But, I have the Irish hair, forehead, and chin.