It definitely is possible to get sharp shots handheld at that focal length, albeit you will need faster shutter speeds as your subject movement is the issue as much as camera shake even if you have Shake Reduction as this only stops camera movement, not subject movement. I have been using my Nikon 400mm f2.8E FL VR lens plus 2x teleconverter handheld with no issues. These have also been cropped about 25% meaning the effective focal length is more like 1,000mm.
D810 + 400 f2.8 + 2x TC, 1/800sec, f8
D810 + 400 f2.8 + 2x TC, 1/800sec, f8, cropped about 15%