Let's say that the humans involved, and their shits, are of a regular size. What you have described is a macroscopic process. Some things work differently at different scales. If you scale your humans down to the size of CO2 molecules then you are describing a microscopic process. It is known more commonly as Maxwell's demon, and it does not work. What you are describing is an attempt to fight entropy directly. The shit would not only win, it would probably hit the fan in the process.
On the macroscopic scale the loss would not be visible in terms of the placement of the shit, but a careful observer would notice changes in the temperature of this shit, and the humans tasked with its shovelling. The heat displaced due to the recognition and rearrangement of the shits would be insignificant. The number of shits given by the shovellers at any point in time would be large. But scale is a fickle mistress and the ratio of useful work (shits given) to heat displaced would drop to zero as we approach the state described before you used your analogy: the net result of your attempt to blow this off as simple is a large amount of hot (carbon-rich) air, but no shits-given at all.
It is not every analogy that works: sometimes the detail removed are critical.