Diamond Shoals appears to constantly have waves because it is where the two major east coast currents meet, the Labrador Current and the Gulf Stream. The shoals are really just big Victory At Sea conditions over shallow sand bars with waves coming from every which direction colliding with each other and the sand. If there are real waves around they should be breaking better somewhere else in the area considering how many beach shapes and directions there are nearby. Surfing there would probably be more of a novelty wave kind of thing rather than being the best break you could find. Not to mention that things are so dynamic there with the sand shifting constantly. That said, it can be surfed. This is more on the south facing beach rather than the shoals though:
You can probably get to the point even when it is closed off for "resource protection" if you are willing to hike some. We were in Buxton last July 4 week. They had beach access blocked from both directions for vehicles and pedestrians though the point itself was still open. We walked out at Ramp 44 and along the beach until we got to an area about 1/4 mile long where we had to go feet in the water (NPS jurisdiction ends at the water line). Though it was a bit of a trek, I have to say it was quite awesome and well worth the effort. I had never been there before without the place being covered in 4x4s and fishermen. We were literally the only ones out there! Swam 30 yards accross a channel to one of the low tide shoal islands and body surfed the only halfway clean wave around.