Yes, the brown wire is what the regulator uses as a reference to regulate the battery voltage. Some regulators use their output wire as the reference, so those don't need a connection to the brown wire. (The reason they use the brown wire, and not the output wire, is some detection circuits may use a little power, and that would drain the battery while parked over a long period.)
The brown wire has battery voltage on it when the ignition switch is turned on. It has no voltage on it when the ignition switch is off. So any voltage source that acts the same as that should be ok to use.
One other issue that comes up from time to time...
If the fuses are dirty or there are bad/dirty connections in the path to provide voltage to the sensing wire of the regulator, the voltage on the brown wire can be reduced. This will make the regulator compensate by making the voltage higher to the battery. In the long run, this can overcharge a battery as well. So it is important to have good/clean/dry connections throughout the system.
I avoid dielectric grease as that can wick into some connections and act as an insulator, causing the exact problem it is trying to prevent.
