From what I gather, the marina is operated by Kentucky State Parks, the game laws (hunting is allowed in portions) are enforced by KY fish & wildlife. The Corps & Fish & Wildlife both manage the wildlife together.
It would seem to me that the Corps would mainly just manage the dams. I would be doubtful you could carry on/in the dams, but that doesn't seem to be the issue here.
Seems like Yatesville Lake is pretty much a state park.
Edit: Oh yeah: http://www.lrh.usace.army.mil/projects/lakes/ybc/