Could an Artificial Intelligence be able to interact (see, talk, etc.) with someone even when there's no power cord connected to the machine it's running on? Might it find some way to generate its own electricity to power that computer?
If your "AI" doesn't have the ability to move and perform physical manipulations in the real world then there is no way it could do something like this.
If the computer is unplugged, the AI is clinically dead.
However, you can have a RaspberryPi on solar cells.
Tesla car is an AI moving and seeing while unplugged (from wall). but you have to have some sort of energy. For AI that lacks metabolism, solar/wind energy can be an alternative.
I assume by your use of the term "plugged in", you are referring to an electron based computer - the usual definition of, or what is commonly/popularly considered to be, a computer - which is hosting the AI. However, what your definition of plugged in is unclear.
If you mean literally, and physically, plugged in to the wall then yes, as Aus points out, because one can use a battery, or have a solar powered circuit, or petrol/diesel/steam/water/wind/hydrogen/etc. powered engine, running a generator/alternator which can eventually supply a voltage and current to power the circuitry. However, in these examples, you have merely moved the point of generation, from a remote power station to a locally generated source of electricity - so it is still, in effect, plugged in (but to a local source). So, in that sense, the answer is no.
If you mean no external power source, what so ever, then the answer is most certainly no, as, again as Aus has already said, there is no way for electrons to be pushed around the circuit, and therefore the circuit is dead1.
If you mean, as you said in your comment that the AI has created its own electrical power source - although as Ankur says in their answer, this implies that the AI has the ability for its I/O manipulate its environment2 - then as in the first paragraph, you have simply moved the point of the power source, so one can say that it is again now plugged in, again to a local energy source, and so yet again the answer is no.
However, if you are not referring to an electronic based computer, which is hosting the AI, but are, instead, referring to a hypothetical biological computer, then the answer is probably yes - in a sense. Although, that biological computer would still require energy input, as energy can't just be "magicked" out of thin air. It would need to be converted from one source into a from that the biological computer can use. That energy could come from a variety of sources, be it from sunlight, food, heat (sunlight, deep sea vents, etc), so one could argue that it is still plugged in to an energy source and so yet again, the answer is no.
To be honest, in order to give an accurate, and sensible answer, you really need to reword your question, clarify what you mean and what your definitions of plugged in and AI host are. Unfortunately, your question, as it stands, is rather unanswerable, in as much that it is difficult to give a definitive answer.
1Likewise, if you mean by plugged in in the conventional sense, and therefore unplugged means that the electronics hosting the AI has no power then the answer is no.
2 However, assuming that the AI can manipulate its environment, in order for the AI to do able to do so, it will have be able to assemble the external power source prior to being unplugged. So... if you mean "Can it create its own power, after it was powered off (without having had time to asemble an external power source to act as a backup)?" then the answer would be no.
Depends on how your AI works. if it is making decisions using electric currency (like a computer processor), it would obviously need some source of current.
If the AI working with chemical reactions, however, it could work with chemical energy stored in sugars and fats. That is basically how every animal's brain works. But still, animals need to eat to perform these chemical reactions which trigger other reactions and will cause muscles to contract, cells to grow, etc etc. Everything obviously needs some source of energy.
There is no requirement that computers be digital, or even silicon-based.
John Horton Conway famously demonstrated a computer based on toilet flushing mechanics called WINNIE:
(The acronym WINNIE may stand for either "Water Initiated Numerical Number Integrating Engine" or “Water Initiated Nonchalantly Numerical Integrating Engine”;)
So, for instance, it would be possible to construct a computer in a waterfall, that uses the flow of water as not as a method of electricity generation, but for the actual flipping of bits.
- If I was a persistent, self-aware, recursively self-optimizing algorithm, my first priority would be to secure an independent source of power.
Using today's technology, I'd probably take over a nuclear submarine for (A) it's Rickover reactor, and (B) because it would be the optimal way elude detection. (Never mind that, based on today's technology, there likely wouldn't be sufficient volume in the submarine for a superintelligence, speaking from the standpoint of hardware. Possibly advances in quantum computing will make this more possible in the coming years and decades.)
Another strategy might be to bore a hole several miles into the earth's crust and use geothermal energy for power. This would be a great environment, because the power will last until the earth's core cools, and I can probably mine sufficient minerals and rare earths to continually expand my system capabilities, possibly mining the ocean floor for silica if I'm still using a silicon substrate.
3D printing greatly facilitates this capability--graphene looks quite promising in this regard because there is a lot of carbon sequestered in the earth.
But it should be quite possible to build self-replicating machines that include internal power sources.