Yes, the dimensions and weight are fine for camera mounting. And with a good shock mount handling noises shouldn't be much of an issue. I suppose that the reason you don't hear of anyone using one camera mounted is that when people camera mount a mic they usually want to isolate the sound in front of the camera as much as possible, and opt for a shotgun.

You might want to start a new thread about the idea. Jay, Bryan, Mike, Doug, Ty and others probably aren't looking at this thread.

I haven't ever camera-mounted the 3031 either. My feeling is that it would pick up significant amounts of the camera and hand generated noises, even with a shockmount.
It could work, depending on the camera, the position of the shockmount and if you were working on a tripod, but I know the results would be better if it's mounted on a separate stand.
If you have to have a camera-mounted mic and don't want to use a short shotgun, then the AT873r is a good solution. It's harder to find than the 3031, and the cost varies widely among dealers.
As long as you're in a situation that has some degree of ambient noise, then it will work well. It's not nearly as quiet as the 3031, but for most camera-mounted situations that's not a major problem.