CTI has a computer rooom with free internet so you can keep in touch with family via email daily if you wish. Or, yes, use the Contact Us # and they will transfer the call to your room and there is voicemail on the phone (red light appears on phone if you have a message).
It's just like any other hotel with a switchboard operator that calls the phone in your room, and there is Voicemail that you can set up on the phone if you wish. I'm not sure how someone would come and get you - unless you are going to tell the switchboard or front desk where you are at all times.
It's best to entrust someone at home with keys, medical notes for minor children, Pet info, and so on- who is equipped to handle an Emergency, as there really is nothing you can do from so far away.
You can also add International Call Plan to your phone for the month of your vacation for about $5.00 extra, depending who your carrier is.