Hello,
I am replying to your question rather too late for it to be useful to you in the short-term, but your question has value for the group so I will weigh in on it anyway:

Sending cover letters to the adcom prior to application is not the "done thing" here in the US either. Nonetheless, some interaction with the admissions offices of top business schools is permissible -- within the formats they offer.

Most b-schools have a generous system of organized campus visits, in which you will meet admissions representatives, sit in on a class that has been arranged for you, often be connected with current students, etc. Many top business schools (particularly Cornell, this year), very much encourage prospective applicants to immerse themselves in the school's culture and they value the steps you take to do so. You can see that a cover letter would not be particularly effective in this context, as you can easily write the exact same cover letter to multiple schools and just change the name of the school. Each top MBA program likes to see you work hard to get to know them.

For an overseas applicant, however, arranging on-campus visits can be complicated and expensive, so it's not a deal-breaker if you can't do it. The schools do have traveling representatives, and they try to make lots of opportunities available to you to get to know them in person, even overseas.

To summarize, replace the idea of a cover letter with a more face-to-face form of outreach, with the emphasis on you getting to know them rather than trying to simply get their attention, and research what each school offers to make that possible for you.

Good luck!
Margaret Strother