Yes, it is very possible. In fact, the blockchain technology is currently being in use by many healthcare providers in various ways. There are also countless of crypto projects whose focus is the healthcare niche. The healthcare niche is the focus of such projects as Docademic, Medicalchain, Medichain, Mediccoin, Medibloc, and many more.
I guess it is not only right but better for a patient's data to be stored in blockchain. That would protect its privacy and security even more.