Many of our customers do (I work in HIPAA-compliant hosting), so I can tell you it's an alive and well thing. Many forms of patient data don't really fit well into relational data structures, so it's not surprising that Mongo (as the most "popular" non-relational db) is common in healthcare apps now.

Most healthcare apps are not "large" in nature and often have way more writes than reads, so many of Mongo's weaknesses don't show themselves in those applications.