Hi Peter,
If BOE still works after joining the domain then so should AD authentication setup.
If however the hostname no longer resolves properly then you could have an issue. In general the hostname isn't hard-coded anywhere and the SIA that starts all the services and they pick up the local name reported by the OS. It's unlikely that the name resolution should no longer work (unless the hostname is actually changed).
You will find the hostname in the bootstrap file and the Tomcat applications properties files (for the initial CMS) but you should be OK I would say.
Thanks,
Bill