Do you have that file? If not, then unset SSH_AUTH_SOCK
will work just as well.
If it does exist, then I suppose it has good chances of working correctly :). ssh-add -l
will try to use that socket and list your keys in the service (or list nothing if there are no keys, but it would still work without error).
Maybe consider static ip assignment in your DHCP server (e.g. internet router) if at all possible… Then you can add a name to it to
/etc/hosts
.Alternatively you could use Avahi to provide mdns names to your local network