Would you do that? Why?
That aside, my approach with Linux/Docker is to have a "fat" host system that is open to the outside world, terminates SSL, load balances and proxies the containers' services (nginx), and provides global services are either shared between containers (Postfix smarthosting to Sendgrid, DNS cache, rsyslog), or services that can manage user/service isolation well enough on their own (PostgreSQL). Containers run mostly applications, or services that I need in multiple instances or versions.
I do containerize Redis, as it can't be safely shared across multiple services (no privilege isolation, too easy for one service to DoS the other with a blocking operation), but then I don't consider Redis to be a database – it's rather a "shared state server", kind of a more sophisticated memcached.
However, I understand the approach of CoreOS, which minimizes role of the host OS. In this model, host's only role is to support containers, and every other process needs to be containerized. From this point of view, Postgres is an application. This way, I can flexibly run multiple version of Postgres, try to upgrade it without needing to set up separate host service, and so on. Personally, I wouldn't feel comfortable with that, but I understand how it could be useful.
Regarding storage performance, database's data directory would need to be a volume anyway (to be able to upgrade database without trowing away the data). A volume is just a `mount --bind`, without any aufs layers, to any point of the filesystem, so it doesn't seem to me that i/o performance hit would be noticeable…