Hamachi [logmein] is a VPN service, right?
I recommend you find a distro that has instructions on how to use Hamachi for making a server.
In the end, connecting to MineOS will just mean you having access to port 22, 8443, and 25565. Getting a server up with these ports listening is separate from the VPN component, which you’re asking about.
So as an example, you can use tutorials like this: https://mikeduckert.wordpress.com/2013/01/08/set-up-minecraft-server-with-hamachi-running-linux-mint/
Linux mint can be used (ubuntu based versions are available) which means you can also use the Ubuntu-based instructions for installing MineOS. If you’re using MineOS Turnkey (which is based on Debian), it’s likely you can use these instructions as-is.
At any rate, Hamachi doesn’t need to integrate, in any way, with your MineOS installation. Both are set up separately and independently. The former makes the latter accessible, the same way as if you were local.