John, envision a simple two-way biwired speaker, the speaker having a capacitor in series with the tweeter and an inductor in series with the woofer. An essentially identical full-range VOLTAGE waveform will propagate from the amplifier to both sets of terminals on the speaker, as I indicated above. However, since the tweeter and its associated capacitor are in series with the wires that provide a path between the amplifier terminals and the high frequency terminals on the speaker, low frequency CURRENTS cannot flow through those wires. Whether that capacitor is within the speaker or "before" it makes no difference with respect to that current.
Likewise with respect to the low frequency section of the speaker. The inductor will prevent high frequency currents from flowing through the wires connecting the amplifier to the speaker's low frequency terminals.
One can hook a loudspeaker up to your supposed treble run and signal will be full range to loudspeaker.
Yes, because the full range speaker will have a low impedance across the full frequency range. Whereas in the biwire situation the impedance looking into the high frequency terminals will be very high at low frequencies (resulting in little or no current flowing at those frequencies), and the impedance looking into the low frequency terminals will be very high at high frequencies (resulting in little or no current flowing at those frequencies).
Or simple swap of treble run to woofer would prove my point.
Low frequency currents will flow through whichever wires are connected to the low frequency speaker terminals, and high frequency currents will flow through whichever wires are connected to the high frequency terminals.
Regards,
-- Al