A direct answer to your question: YES!
I am a retired USFS Recreation and Wilderness program manager. My wife and I were camping at a Corps of Engineers campground which actually remained open during the last government shutdown. It was a normal camping experience.
While we were out and about, we came across a USFS campground that was closed because of the shutdown. There was no sign or anything, but the gate across the entrance road was closed. We thought we'd like to check the campground out to see if we'd like to camp there in the future. So we parked our pickup truck outside the gate and walked around the campground loop to look at the sites. During this time, I needed to go to the bathroom (you know the problem with older guys!) so I went into the vault toilet to use the facility. When I came out, a USFS Law Enforcement Officer was standing there talking with my wife and telling her that we couldn't be in the campground because of the shutdown. We explained that we weren't camping, just walking through the area to look at the camping spurs. Made no difference. He escorted us out. We returned to the COE campground (also a US govt. operation) and continued to enjoy our camping experience there.
So yes, the campground was closed (and blocked) from anyone entering with a vehicle, and they even said that we couldn't walk through the campground.