To qualify for a degree at each institution, you must complete all credit hours at the two institutions. This means that you may not transfer credit - from AP or IB tests, or from other colleges or universities. If you have taken AP/IB courses, or have taken a course or two elsewhere, you may use those courses for prerequisite or breadth requirements. They can't count towards the total number of credits required for your International Honours degree.
For example, if you got a "5" on the European History AP exam, you could skip History 111 and enroll in a higher level course at W&M. It would also meet Programme's knowledge objective in Western History and fulfill that breadth requirement. So, test and transfer courses still give you a boost, but you don't get the credit hours on your transcript. There is no graduating early in this program.
You should also be aware that the same policy applies for study away/study abroad programs. Unless they are from courses offered by William & Mary, you may not transfer study abroad/study away credits.
For more complete information, please review the Programme Guide and Catalog Supplement.