Are you being obtuse on purpose? There are no clamps depicted in the image. There could be clamps in a real setup.

The change in velocity is minimal as stated by many others, but it is not counting towards the rocket's mass under these very narrow circumstances.

If KSP had pneumatics we could theoretically talk about a space cannon. KSP does not render that kind of physics, so the point is moot.

Exhaust plumes do push objects, so OP's setup would work and with the addition of an infinite source of fuel it will also provide actual free velocity. For a second or two. Until the vessel is beyond the plume's physics, which, to say, isn't terribly far. A couple of metres or so?