You are looking for an old style mainframe, NixOS is about configuration and programs installed.
Depending on your need you can achieve what you want with just some ssh connections and stuff, you can even tunnel a graphical interface!
However if you are just looking for file sharing and syncing, you can just make and http or ftp (tho this protocol is not recommended anymore) and access it across several computers.
You can also use auto-sync processes (IIRC "rsync" is one) or just a syncing daemon and a git repo.
NixOS can help you, but only on the way you apply a configuration. I personally just have my own setup file in github.