As long as the skilled nursing facility or hospice care facility has a contract with the Medicare program then yes the Medicare will pay for the hospice care in a skilled nursing facility.
Medicare will not pay for the room and board portion usually though but will pay for the hospice care so you will usually have to pay out of pocket for the room and board at the skilled nursing facility.
Some other health insurance might cover the cost of the skilled nursing facility room and board while the Medicare program covers the cost of the hospice care at the skilled nursing facility.
The patients doctor will have to get in touch with the Medicare program to approve the care needed by the hospice care in the skilled nursing facility though.