So in principle it could work, but the problem is that these days, the big players are all doing high frequency trading with algorithms that try to predict market swings. And the big guys have an advantage: they are closer to the stock exchanges. They trade so fast that speed-of-light limitations affect who gets the trades in first. So I think the only people who could win with an LLM technique is someone who doesn't need to pay commissions (a market maker, Goldman Sachs or similar) with access to real time data, very close to the exchange so they get it fast.
(tongue firmly in cheek) Here is a bastardization of a memory of some video interview with a quantitative analyst, from over a decade ago:
"Show us your yield data and we'll TELL you your weather and political climate."