In the sense of "take control", not really.

In the sense of "monitor various actions/activities", then yes (at least in theory).

There have been some studies and experiments where you can determine what a CPU is doing or executing by monitoring very finite changes in the current draw of the power supply. To do this with any accuracy, you would have to install a rather precise power monitoring device on the circuit powering the PC itself, and most likely on the power cord going directly to the PC (so as not to pick up electrical data from other devices on the same circuit).

You would also more than likely need brief physical access to the PC itself, so that you could calibrate to various CPU states.

So, it is somewhat possible, but not in any practical application.

It's possible (but extremely improbable). By which I mean, if anyone has the capabilities to do that, they're just as likely to extract whatever information they need from your brain, or rewrite your mind to make you want to give it to them.

Or realize that they have better uses for their time.

Ordinary networking attacks could work if the system in question uses EOP (ethernet over power).

Huh?

Well, if you have control over the power, you could probably launch some pretty effective DoS attacks.