Oh yes you can do it! Start your day out earlie and plan on traveling late, and you can do it. Your only delay will be the ferry crossing from Cedar Island to Ocracoke. Do you have the ferry schedule? If not you can get it by calling 1-800-ByFerry. Or
http://www.ncdot.org/transit/ferry/routes/download/FerrySchedule.pdf Don't forget to stop and visit the Chicamacomico Life-Saving Station as you pass by.
Good Luck, I know you will have a good time!