Theoretically speaking?

First of all, white matter is myelinated axons (myelin is what makes it white) - the gray matter is the neuron/axon itself. In response to your question, the answer is sort-of, but it's kind of complicated.

In metal wires, charge is carried by the movement of electrons. Cells are pretty crappy at carrying electrons - instead, they move charge by moving around positive ions (mostly sodium and potassium) and negative ions (mostly chloride). This is because cells are mostly filled with water, and pure water is actually an insulator (it just happens that water in the environment almost always has dissolved ions, which makes it conductive, and dangerous for us to drop a hairdryer in). So, if you just hooked up a length of axon in place of a wire, it wouldn't conduct much of anything, because the resistance would be very high.

If you had a living axon, however, sitting in the right electrolyte solution (basically, the same as what you'd find in a person), you can make it carry a current. I'm not going to try to explain how a neuron works here because it would take too long, but in essence, the cell moves current along by moving ions in and out of itself through channels that are opened and closed with changes in voltage (which is caused by shifts in the concentrations of ions inside and outside the cell). This process is a lot slower than electrons zipping around, because the channels have to physically open and close, and unless you have a humongous axon, you also can't carry a lot of current, because you simply can't move enough charge. However, for signaling, you don't need a huge current, so it works fine for its intended purpose. You can hook the living neuron up to your circuit because using your electron-carrying wires, you can change the electric field around the neuron enough to activate the voltage gates, essentially converting your electric current to an ionic one, and carrying it down the neuron; at the other end, the ionic current can induce an electrical current in the wire at the other end. In fact, you can pretty accurately calculate the behavior and electrical properties of your neuron "wire" with something called the cable equation, which models the neuron by representing it with a bunch of electrical parts. If you are that curious, take a quick look at the link here, and you'll see that it is much more complicated than just a plain wire (but don't expect to understand it unless you have had college level calculus and physics): http://en.wikipedia.org/wiki/Cable_theory

Scientists have engineered microchip devices which can stimulate different areas of the brian so that it can treat illnesses like depression for instance.

White matter is the brain is however still neurones like all other brain matter, and so the whole brain is one big circuit in that sense.

The chemicals are the messengers which act between axons and synapses etc, are what make the electrical activity in different part work the way they need to.

There are electrolytes as well, which regulate the other chemicals (minerals or salts).

Oxygen and glucose is the more critical for brain functions, which make the whole system work via ATP in the mitochondria of the neurones.

CREED

Yes. White matter consists of nerve fibers each of which is a bio conductor.

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