My install is this Thursday for the wall connector so I'm hoping they know enough about this to explain what I can do and if it will monitor everything. I don't have my model 3 quite yet so I can't actually test it unfortunately.
The Neurio measures both AC voltage and current. If you look closely you'll see that the Neurio monitoring your solar is powered from a breaker somewhere: On my PV system, they installed an entirely new breaker in the sub-panel for that - it not only allows voltage measurement, but power for the unit as well.
In the gateway the Neurio is clearly powered elsewhere - but I didn't really check to see where its mains was connected. Since this Neurio needs only monitor grid power and current (on the "grid" side of the disconnect relay) it is entirely possible that it goes offline if the grid power fails - but this would be unimportant when operating in island/stand-alone mode as the load of the house could be calculated in that instance by subtracting the power produced from the PV system from the load/charging of the Powerwalls as determined by the Powerwalls' built-in voltage/current monitoring.
It's worth noting that the Powerwalls themselves power the BUG (Back-up gateway - the computer part in the gateway), apparently in a "diode-OR" manner if you have more than one Powerwall (e.g. any single power wall will supply DC power to it). (Note: This also means that even if you completely "power down" the Powerwalls by opening breakers/switches and turning them "off", the BUG still remains powered at all times as long as there is at least a small amount of power in a battery.) It is possible that the Neurio is powered from the same DC source as the BUG in addition to/instead of the AC mains (on the "grid" side of the disconnect relay) just in case they (Tesla) want to the grid-monitoring Neuro to remain powered even during a grid failure.
Because the Neurios seem to be connected either wirelessly or via a multi-drop RS-485 serial interface, it probably wouldn't matter if the "grid Neurio" was offline during a grid failure - but keeping it powered up would allow the system to differentiate between a grid failure and loss of communications to that "grid Neurio".
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I suppose that the ultimate answer to you original question is:
No, you do not need to change anything related to your Neurios at all to add additional house load(s).
In my system, my house wiring is now connected to a sub-panel of the original breaker panel to accommodate the fact that it was impossible to wire the isolation relay into the original combination breaker panel+meter. Because of circuit relocation, here are now many open slots in the original panel and I could add circuits to this panel - but they would be "unprotected", that is, not backed up by the Powerwall system. Because the original panel is "outside" the domain of the Powerwall (e.g. not backed-up) there is absolutely no need for the Powerwalls to even know about those loads, so no need to change the Neurio in that case, either.
Now, if you add more solar, you would simply route the wires from the new PV system/breaker inside the same two CTs (current transducers),
paying careful attention to phasing so that the two currents would add to each other rather than subtract - and that's how my two inverter systems are monitored. One would need to add another Neurio only if the wiring of the "new" PV system were not in the same panel as the original and could not be routed through the existing CTs. By using a single Neurio the Powerwall system can only detect the total power from the PV system and not from each inverter, but it only needs to know the total. (For monitoring each inverter? I have an app for that!)
CT