I'm not even an LLM researcher. But I believe you're correct; I just don't think the paper provides any meaningful evidence on the subject. From the structure of the model we can tell that dots can do more computation than no CoT and less than full CoT. What we don't know is how much of the performance gap between no CoT and full CoT would be recovered by an LLM using dots. The paper answers that question for a tiny transformer, but it's so different from an LLM that extrapolating to LLM scale is purely speculative. In other words it doesn't give us more information then what we can already determine from the structure of the model.

For the record, the original claim was that "you can replace intermediate tokens with single character chains and still get the increased precision", which I read as saying you can get almost all of the benefit of CoT with dots, not just some unknown fraction of it. This claim is true for the paper, though probably only because the benchmark was saturated (and training difficulty was also higher, as they mention). But the claim is unlikely to be true for LLMs, if only because they presumably do sometimes need to perform "long running calculations", and they also have plenty of unsaturated benchmarks.

(The other part of the original claim, that CoT is "not a representation of a model’s logical path", is more complicated. It's clearly not guaranteed to match the model's logical path, as we have seen with other research into actual LLMs. But it does seem to be correlated with it, presumably more so for more complex / long-running tasks.)