I'm sure it is possible, but where do I start with this fiddling? I would need to start X.org and automatically launch Kodi... Can I do this without logging on? Is there a desktop environment which would be best suited to deploying a single application ?
SLiM has a auto-logon function, you could use that. Kodi itself could then be started from ~/.xinitrc. OpenELEC starts Kodi with some specific options in order to start it without Xorg. That's also a possibility, you could use that to start Kodi from rc.local.