Health data is very far from this idealized anonimization-friendly case. It is some of the most specific data avalible about you, and it can easily be abused to disadvantage you in ways you can do nothing about (insurance, job prospects, social standing, even as far as getting your life threatened by people who disagree with things like sexuality and abortion)
Im sure Google appreciates your faith in them. But you should carefully consider the consequnces. Once the information is out there, there is no getting it back.