Well TEMPEST shielding is basically a Faraday cage so the answer is yes.

There is always a way. A program could take control of the LEDs on the PC and export data by flashing them in certain patterns.

A Faraday cage would not let light escape. That is the definition.

How does a Faraday cage block visible light?

It’s a poor word choice I believe, a faraday shield also blocks light, while a cage can be seen through.

Modems in the olden days used to have LEDs to show traffic directly attached to the TXD and RXD lines coming off the level shifter, and therefore directly showing the presence or absence of a bit stream on the serial port.

With a suitably tightly focused telescope you could pick up the LED blinking and decode the data going over the port.

Now all you need to do is get a light sensor within line of sight of the LEDs, and away you go.

Yeah, in fact, Flashing led at several MHz is indistinguishable from constant on led.

Speak for yourself. My air gapped servers are inside a black hole.

Yes, Faraday shielding is one of many considerations when building a SCIF or other EMSEC zone.

Putting it beside a Tesla coil would work too, make more noise than the computer does and you'll bury the signal.

Of course, now you've got a Tesla coil in your data centre, which will bring you a whole new set of Interesting Problems to cope with.

Tesla Coils from Command & Conquer are oddly relevant here: Attack, don't defend. Don't build Tesla coils. Build tanks. Don't let your opponent decide the terms of your inevitable confrontation. Turtling never works.

Yes, and you can defend against any single attack that you think of in advance, but you will still be surprised by one you haven't thought of that was used by a sufficiently resourceful attacker.

If you want the thing you're isolating to be useful to you at all, you will need to have some physical connection between the inside and the outside, i. e. a hole in your air gap.