I have done this type of work which I would term a Live-in Home Health Aide. Usually the Agency policy defines what is expected of the Aide working a 24-hour "live-in shift." The expectation is the Aide sleeps when the client sleeps.
I have read the manual at two Home Health Agencies and they both clearly outline requirements such as a separate room, private bath, 7 (or 8) hours uninterrupted sleep, place to store perishable food, etc. I would check with your supervisor if you are working that type of case and see what the policy states. The case manager is supposed to make sure all of these things are in place before writing a care plan for live-in aides.
On the flip side, most health care providers have policies that prohibit sleeping while on the job. This actually means no sleeping even when on break, not even in the breakroom. So I'm really concerned whether you should be sleeping at all as an "Overnight CNA." I've worked my share of cases when I arrived at 6:00 AM to relieve the "Overnight CNA" and had to shake her chair to wake her up and tell her it was time to go home.
For real world advice, if you like the client and like the pay and are allowed to sleep, say nothing and make the best of what you have. As soon as you complain to the office and they approach the client, she/they will find someone who will work the case and sleep on the couch.