YSOM did very well with McK this year, 25+ for McK internships alone. Given that there are only around students 150 recruiting for consulting, that's not bad. If full-time recruiting takes twice as many students (this is historically the case) then that could mean a third of the consulting class goes to McK alone.
However, the key stat is that there were over 100 McKinsey OCR interview slots in a consulting cohort of 150 (note that intl students may go off-campus). Once you're through to interviews, its more about you and your prep than the school.
Further, I am an intl student and I secured two intl internships by emailing the CEO of my target firms directly (both firms have 50k+ employees but do not take on MBA interns), using the company's email-naming conventions I found online. They both replied and invited me to successful meetings. I am not sure that this would have been possible without the Yale brand.