To be honest, I exited the article thinking the answer is "no", or at least, perilously close to "no". The same amount of work put into a conventional solution probably would have been better. That cross-product "solution" is a generalized fix for data generation from a weak data source and as near as I can tell is what is actually doing most of the lifting, not the LLM.
That said, I'm not convinced there isn't something to the idea, I just don't know that that is the correct use of LLMs. I find myself wondering if from-scratch training, of a much, much smaller model trained on the original data, using LLM technology but not using one of the current monsters, might not work better. I also wonder if this might be a case where prompt engineering isn't the way to go but directly sampling the resulting model might be a better way to go. Or maybe start with GPT-2 and ask it for lists of things; in a weird sort of way, GPT-2's "spaciness" and inaccuracy is sort of advantageous for this. Asking "give me a list of names" and getting "Johongle X. Boodlesmith" would be disastrous from a modern model, but for this task is actually a win. (And I wouldn't ask GPT-2 to try to format the data, I'd probably go for just getting a list of nicely randomized-but-plausible data, and solve all the issues like "tying the references together" conventionally.)