Let's assume I'm coordinated enough not to hit anyone or anything with the tripod.
I'm concerned about the DSLR/plate/head interface. Assuming everything is properly attached and tightened, can I balance my tripod legs over my shoulder like you would a gun or rake or other long object and have the DSLR hanging off the end without fear of it coming off or otherwise damaging the head.
This is the actual head I have, though I'm more concerned with the safety of this practice at a general level.
There is no such thing as absolute safety. But you are probably fine doing this.
A few things to consider:
Sure, I do this all the time.
Here is a tip: Thread your camera strap through the tripod legs. This way its 1) out of the way, and 2) if for some reason the quick release fails, the camera will drop only as far as the strap will allow. Good for an OMG! moment, but no sickly metal/glass crash sound at the end.
Honestly, this is really the only time I actually use my neck strap on my camera. For the record, that is a Kirk BH-3 and it has NEVER failed me. [insert crappy phone photos here]
I'm going to disagree with the others. While the camera locking mechanism is unlikely to fail, you are putting stress on the head from forces that aren't present during normal use of a camera and tripod.
Those are a lot of points of failure.
For example, a camera and lens combo totalling 1.5kg (3 lbs). You may have a tripod head rated for 5kg (12 lbs). But the forces you are creating bouncing that camera at the end of a tripod over your shoulder may easily exceed that.
Will the camera come off? Unlikely. But you could end up stripping threads, damaging your camera mount, or weakening the tripod head locking mechanisms so that they are not as effective as they once were.
Yes professional photographers, especially sports photographers, can be see carrying their gear in this way. But they may not have the luxury of time to repeatedly detach/reattach a camera, and as @unapiedra said, they'll have sufficient insurance to repair any breakages. Going through gear is what they do.
In general the answer is yes, given this is primarily how professional sports photographers carry cameras/lenses - monopod slung over the shoulder with the lens and camera attached.
This is about the best photo I can find to demonstrate this:
http://naturephotography.fredhurteau.com/images/camo/PadOnShoulder.jpg image (c) Fred Hurteau, naturephotography.fredhurteau.com
They're using heavy duty pods/plates I can't speak for the specific model you have linked to.
With a lightweight head, I would be more careful. When I carry my camera on its tripod, I try hold the camera at my shoulder (or resting on my shoulder), while letting the legs point straight down. Usually, I will have my arm on the legs. I carry it in a way that keeps the vibrations and torque on the head to a minimum while I am walking.
At some point, practically all material that flexes is going to crack. It may start as a small, invisible crack, but once a crack occurs, it introduces points of high stress that lead to failure. Stronger material or sturdier design will minimize risk. A big camera or a heavy lens that can place large torque on the head can be more of a problem than a lightweight camera with a short lens.
I wouldn't carry my camera with a heavy long lens for long distances in a horizontal position (like Matt's picture shows) unless the mount is very sturdy (like Matt's picture also shows.) Every bounce that the tripod and camera experiences translates into a strain right at the head that can lead to failure. Carrying it vertically puts all the strain into compressing the material, rather than flexing it. It's less likely to fail that way.
Assuming like you said everything is tight and in place then sure there is no need to worry about you camera falling off.
I often carry a monopod with a Nikon FX body and a 400mm f2.8 weighing in at 11lb, over my sholulder around stadia with fans and children running about, some of them knock their heads on the lens or trip over the monopod leg, even though it is onlt 1/2 foot infront of me. But it always does more damage to them and the camera and lens stay in place.
It all comes down to how much you trust your tripod/head. Evidently lots of professional photographers do it. I personally don't carry my camera that way, but then again my tripod is about 10x cheaper than my camera.
In general, I'd say it's ok. Just make sure everything is tight before slinging, and try fiddling to see if you can easily/accidentally knock the camera out of the QR mechanism.
I use the Arca-Swiss QR system with plates from Really Right Stuff. Many of their plates feature a stopper screw which is an extra safety measure exactly for this purpose. For example, take a look at the underside of this Nikon D300 plate (the second photo). Notice the little silver screw, which stands up just a little bit from the plate. When mounting the camera on the tripod, this screw keeps the camera from sliding off in one direction, even if the clamp isn't fully tightened. When carrying, just make sure the side with the stopper is "up" and there's a little extra assurance that you won't lose your gear.
