The heaviest lens I've used hanging from a strap attached to a camera body is a 60 oz./1700 gram EF 70-200mm f/2.8 L IS II with tripod collar and lens hood. I've had no real problems over years of fairly hard use with this practice.
However, there was a time when I did the same thing with a 2.5 lb/1150 gram monopod/tilt head combo attached to the lens' tripod collar. The combined weight of lens and monopod/head was about 6.25 lbs./2800 grams. The tilt head was turned so that the compacted monopod was pointing straight down in the same direction as the axis of the lens when I was not using it.
After only a dozen or so outings using this method, the connection between the lens and camera, a Canon 50D, started showing excessive play and I ceased using the practice and began attaching the monopod to my belt when not in use. It turned out that most of the wear was to the surfaces on the 50D's mount ring where it contacted the lugs on the lens' mount ring, with a much lesser amount of wear to the lugs on the lens' flange ring. I guess it it possible that the total weight was not as much an issue as the fact that the weight of the monopod was off-center to the center axis of the lens.
With the AF-S Nikkor 200-500mm f/5.6 E ED VR you're talking about a 5 lb./2300 gram lens!
Personally, I would not risk it.
As to whether there is more stress on the mount connection with the lens hanging vertically or extending out horizontally:
- There's more shear force applied to the mount when the lens is extended horizontally. The pressure is greater on smaller portions of the connection at the top and bottom of the ring. The force near the bottom of the ring is compressive, the force near the top of the ring is tensile. The farther from the mount the center of the lens' weight is, the more each of these forces increase in an offsetting way. The stretching force (tensile) at the top of the connection increases at the same rate as the compressive force at the bottom of the connection.
- When the lens is hanging vertically the load is more evenly distributed around the entire ring, with almost all of the force being tensile.
Related: Are there any official specifications regarding the torque for camera mounts?