Hi P,
Schools care about many things, but two at the top of the list are your uniqueness and whether you will fit with the culture of the school. Being a URM could therefore help you in the uniqueness category.

However, in the end what really matters is how you sell yourself. Do you have a coherent story on what you want to do after your MBA that makes sense when considering your past. Can you show why your personality matches Yale's culture and how you're going to fit in with other students?

Another really important idea is that how you say something is often just as important as what you say. Have you written essays that come to life? I've had a number of students who came to me with great backgrounds and stories, but who didn't know how to really bring their best aspects to the front.

In sum, your competitiveness is going to depend a lot of how well you write your essays. As far as the AWA and IR score, I wouldn't worry about those. Some schools have come out and directly stated that they don't care about the IR section at the moment. Your GMAT score is below the average for Yale, but good essays and life experiences can often make up for a slightly below average GMAT score. I've had several students get into top schools (Columbia, Stern, INSEAD, etc...) who only had around 650 on the GMAT.