Docker switched to Alpine Linux by default, so there's that hurdle... Not to mention the giant legal question mark of loading CDDL code into a GPLv2 kernel.
One of the ideas of containers / virtualization is that the host operating system (Ubuntu, in this case) has as little to do as possible with the VM / container (Alpine, in this case).
Running an Alpine container using Docker on an Ubuntu host will work just fine.
That's for the container package management system, not the host storage system.