My DD has been looking into this nomination source as well. Not to sound too pessimistic (I know it does though), what are the actual odds of receiving this nomination?
The Vice President is authorized to nominate individuals to the United States Military, Naval, and Air Force Academies but can not nominate to the U.S. Merchant Marine Academy and does not nominate to the U.S. Coast Guard Academy.
He may have a maximum number of five nominees in attendance at each authorized academy at any one time. Normally, he has one or two vacancies each year.
Let's just say he has 2 vacancies at each of the 3 academies he can nominate for. I don't want to discourage people from trying, but the odds are very long. Personally, I think your time is better spent putting together the best application for your MOC's as possible.