Well, it isn’t the usual thing to do, but I don’t see why there would be a problem.
- Ubuntu Server comes with no graphics support: You’ll need to add the mesa kernel drivers (and maybe other stuff).
- You’ll need to configure mir-kiosk to run as a daemon.
- chromium-mir-kiosk is deprecated in favour of wpe-webkit-mir-kiosk
Good luck!
Edit: @menarcarlos, once you’ve worked out what graphics packages you need to add to Ubuntu Server could you document it here for the next guy that asks?