In the states, it is going to depend on if it is a private or state campground. And for each depends on the state. Some state parks have hiker biker policies while others do not. West Virginia State parks do not have such a policy but I was told by an attendant , in the event the site is full, hang around till he leaves for the night and then go pick a spot.

In PA, some private campsites have hiker/biker policies while others do not. Which frankly I don't understand that if you are on a bike or hiking route why you would not have some out of the way patch of land for folks looking for a last minute campsite.