What is the AppleCare agreement's location?
You should pick the location/country you've bought your Apple product.
The AppleCare states clearly you have "care" around the entire world, as they state even abroad is no problem. You don't have to move your product, as it's part of the Care you're paying for.

My iPad came from Canada and I'm using it in the Netherlands. Registered it first as Canada to avoid problems.