If I show up with a steak and charcoal, will I find a grill where I can cook it?
Sure you will find a grill but not sure if it will be clean enough to cook a steak on it!
I did not see any grills near our camp sites. We had electrical outlets. That was all.
I don't think you'd have an issue if you were properly motivated. Each campsite I saw had a fire pit with a grill over it, mainly for wood fires but there's no reason you couldn't put charcoal under the grill. I also saw a charcoal grill next to the fishing pier at Prairie Branch Camping Area so I'm guessing they have more scattered around.
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