It does not really matter how far it travels.
But no, if the NDS and the US talk with each other while connected to a local switch, the switch learns that, say, the NDS has the hardware MAC address “abc” and is connected to switch port 1, and that the US has the MAC address “xyz” and is connected to the switch port 2. So if it sees a network packet coming in on port 1 from “abc” and being addressed to “xyz”, it sends the packet out of switch port 2, without bothering the upstream router.
This was what I meant in my earlier post regarding
If there is no local switch, the “router” (which is actually both a router* and a switch** in most consumer setups) performs the same function.
Mind you, there is always some control and bookkeeping data being sent around, to keep the network functioning. It’s rarely 100% quiet on a network. This is normal and by design.
In addition, apart from the digital data, network cables are still electrical devices that emit and receive analog interference; this is what people on audiophile forums usually are concerned about. However, that’s what networks and devices on it are designed for, and I would not overly concern myself. It’s usually not much work to compare later by replacing the regular switch with a 3K “audiophile” switch, if you really want to.
* It’s a router because one module of it “routes” traffic between two different networks, the upstream internet link and the local network. It does this on higher levels of the networking protocols, like IP addresses.
** What is commonly called “the router” also contains another module that works as a local network switch for the local devices. This happens on the lower, “dumber” network protocol layer 2, which is based on MAC addresses. Every network device has a globally unique one, and it is fixed for every device by the manufacturer. Every MAC address on the local network can see every other, so this is a very basic identification layer, which the switch uses to send traffic only to the device that needs it. (In contrast, MAC addresses are not routed by the router part - they are stripped out when the router sends data from the local LAN to the upstream internet link)