I suppose it’s possible, but not ideal. You could walk into the trees a bit and find a spot, but I don’t think the ground is clear of brush, etc. The Swain Ridge Trailhead is just down the road, so parking at the trailhead

Not really - the trees in the southwest corner of the field may work for hammocks since they're less covered in brush, but that area of the field is also less flat and gets pretty muddy when it rains.