Transformers naturally have a big part of the network that is unused on any particular token flowing through the model. You could see that by how little RAM ended up being used in llama.cpp when they moved to mmaping the model.
So my understanding is that the tenstorrent cards are drastically more efficient, even on "dense" models like transformers because of the sparsity of any specific forward pass.
Also: I wouldn't bet on AMD accelerators for ML. They've disappointed every time. I would trust Jim Keller, whose every project in the last decade ended up being impactful.
I think the internet access is just to download the driver. It's not some sort of DRM setup where it needs to be always-online.