Upon reading the title I thought about a feature present in most OFP cutscenes (haven't viewed many in ArmA, but never noticed it).
Most people made the camera and then targeted the camera at units. Let's say a soldier, any type. When a soldier walks his head moves up and down so in most cutscenes with camera's targeted on units - the camera got shaky.
This seems to be what you guys are looking for. Brandon, the Youtube movie you link to features the same thing. The camera gets shaky when targeting the AA missile, that is because the AA missile itself moves - left / right and up / down. So a shaky camera is definitely possible, I don't think a shaky 'normal play vision' is possible though.
EDIT: just noticed
this. Might be interesting, as it is more or less an example of the things described above.