I've not seen Kid's Story, but I thought, while watching The Matrix, that the "disruption" to Neo's life signal was basically just him waking up in the real-world.
Morpheus says the pill-virus disrupts Neo's IO signal, which sounds like it could disconnect him from the Matrix, and the process that Neo goes through with the silver mirror ends with him waking up. I take it that the mirror effect is him being taken out of the Matrix. Perhaps it's him connecting with his real body for the first time.
People waking up can't be a very common occurrence, but the system will have to be able to handle it. A body that is to be removed from the power plant but that isn't dead is surely going to be relatively easy to trace as it will be flagged up for special disposal (at least, that's how I took it as he wasn't taken away to Resyk to be turned into food).
The awkward part of this is that they use equipment within the Matrix to trace Neo's location, and it seems that the equipment set up is not trivial, so they must have been looking for something when the Kid woke, which is an impressive coincidence, but probably less of a coincidence than them just stumbling across him floating about after being ejected.