If the patients Physician accepts Medicare and the Physician says that home health care is medically necessary for the dementia patient then yes Medicare will cover the cost of the home health care nurse for the dementia patient.
If Medicare won't cover the cost of the home health care which they should you can also purchase insurance that is used to pay for home health care when needed or even check with the patients health insurance company to see if they might cover the cost of home health care as some might if it's needed.