Big 4 guys (especially Asian or South Asian guys) usually have a pretty slim chance at H/S/W. Given the sheer volume of Asian and Asian-American guys applying, there's more than enough Asian M/B/B consultant types who will crowd the Big 4 guys out. Of course, it's not 100% and even those with M/B/B backgrounds (regardless of ethnicity or nationality or gender) aren't exactly shoe-ins either.
Apply if you want, but just know that they're lottery tickets.
Schools where you will have a more reasonable shot are Kellogg, Sloan, Booth, Columbia, and Tuck. These are stretches but more reasonable stretches. Schools outside the top 8 like Cornell, Yale, Stern, Duke, Darden, Michigan, Anderson and Haas will be your sweet spots.