I don't know about that, mostly because the structure of LLMs at the moment make them incredibly bandwidth-hungry, and also quite sensitive to latency.

You do have some small-scale versions of that, where people link a few smaller computers together to run a larger model, but that usually exists in the form of things like connecting machines via USB4/Thunderbolt, or Oculink, which are much faster and lower latency than a typical internet connection.

There is something a bit like that, with the Kobold AI Horde, but that is still people hosting an entire model and sharing that over the internet, rather than something like Folding/SETI@Home, where you're doing part of the actual calculations yourself.