Absolutely, however the signal current is carried by a conductor that is connected to chassis ground; the shield wire should also (at one end) be connected to ground but it's no more a signal conductor than the grounding conductor in your home is a current carrying part of the circuit.

The reason balanced connections have better noise immunity is twofold:

• They usually have lower input impedence compared to the non-common connected signal side of a single ended input. Lower impedance means lower induced voltage, all else equal.
• In both systems the signal is the differnce bewteen the two wires, however, in a single ended configuration the impedance to common between the two is vastly different by design, whereas in a balanced system they should be closely matched; thus when the single ended system amplifies the difference in the two signal wires, the noise is not significantly cancelled because the much lower impedance to common of the "shell" wire prevented any appreciable noise from being induced on it, therefore there is nothing useful to subtract out. Essentially the asymetrical impedances caused asymetrical noise to be induced.