No, they're not predictive at all. They're generative. A prediction is a forecast based on a theoretical model about a state of affairs in the world. Making a guess what the weather tomorrow will be is a prediction, and a prediction can be true or false. An LLM generates text based on certain parameters, and output it generates aren't true or false, they're simply whatever the system is tuned to produce.
LLMs are terrible at making forecasts or world modelling precisely because they don't actually operate on much of any model or theory, they have no notion of truth or falsehood, they simply generate whatever you want them to generate.
In this specific context, the point is that LLMs and MT "predict" lucid-sounding sentences that incorporate linguistic structure (syntactic and semantic) that are well beyond the predictive abilities of the Chomskyan theory of syntax (which is itself a generative model). In other words, the Chomskyan model of syntax is descriptive of much of the rich variation in real-world human language. But it is not predictive in the sense that it does not provide a constructive algorithm to emit lucid-sounding sentences (and does not attempt to, either).