Not directly related to your question, but I would be careful about passing user health data to the Game Center. I don't have enough details about your product, but here in the States there are strict privacy requirements dictated by HIPAA when it comes to protected health information (PHI). You may not want to tie a user account (in game center) to health activity depending on exactly how it's going to be used and whether it would fall under PHI as defined by HIPAA.

Also, as a diabetic myself, the idea sounds pretty cool. If someone could gamify my regular blood sugar testing I'm sure I'd be more compliant with my testing schedule :)