A faraday cage is essentially a hollow conductor. It does not have to be grounded for the cage to protect whatever is inside it from the induced voltage of a lightning strike. When lightning induces a voltage drop across a Faraday cage, the charge levels in the conductor the cage is made out of end up neutralizing the effects within the cage itself, as seen in this image from the wikipedia page on Faraday cages:
Also, consider that if the Faraday cage itself were struck by lightning, the electrons, wanting to repel each other, would only travel along the exterior surface of the Faraday cage, leaving the interior untouched. Now, if the Faraday cage is not grounded, it would hold the charge until something that is grounded comes into close enough proximity for it to discharge the static surface charge.
Whether the cage is grounded or not has little affect on its ability to protect its contents. Of greater import is what the cage is made of. A solid conductive cage, like a stainless steel pressure cooker is far more protective than the mesh of a microwave oven or a marine stove's oven, which often has a large glass window. Either of these would leave gaps in coverage.
The static dissipator would need to be grounded, since it is trying to equalize the static electricity with the surrounding area and reduce the chances of a lightning strike. Forespar says this very clearly in their brochure:
Static dissipators may be mounted on any of these points, as long as they are provided with a direct electrical path to ground. If you have already bonded and grounded your mastheads, masts and standing rigging as described above, a dissipator may be added directly to your mastheads.
I have been told that the boat does have to be grounded for the Faraday cage to work or for the bottle brush to work, but I would need to brush up on my physics to answer that for sure.
Tin foil is not the right material to protect electronics. I was told that lead foil is. I have been told that many of the older manufacturers of sensitive equipment put their boards in lead foil.
THis is all hear say.
I am surprised this conversation has not turned into a 'ground or don't ground your boat' debate.