I think the OP means that the discharge order was written at 9am, but for whatever reason, the actual discharge process took hours to accomplish. This happens a lot, like if outpatient services are being arranged, or for obtaining transportation, or if the destination isn't prepared to receive them yet.
To answer the question, yes, I would do it. Just because the patient has a discharge order written does not mean they are discharged. They aren't discharged until they have physically left the hospital, and until that time, if you are the nurse assigned to care for them, you are still responsible for their nursing care. Also, no matter how stable they appear, there could be a change in condition between the time the order to discharge is written and the time they actually leave. Additionally, it is important to document their condition upon discharge.
When I was a CNA, I was transporting a patient who had been discharged. I had just gotten him into the wheelchair and had taken maybe three steps toward the elevator, when he slumped over and became unresponsive. Needless to say, he was not discharged.