Is this the kind of care health insurance will pay for?

This is something that you will need to discuss with your own insurance. They vary widely as to what kind of in-home help is covered, and they all require qualification for care.

If the person has a Medicare Advantage plan, they may be able to get a CNA. Medicare psys for intermittent care but not a daily CNA. Medicaid may be an option but the person has to fit a certain criteria.

You give no details in your profile, like what state you are in, how old you are (Medicare?), and who the CNA is for. Therefore it is impossible to give you any advice. Please provide more info.