> A lot of people would say that LLMs generalize pretty well

What do you mean here? The trained model, the inference engine, is the one that makes an LLM for "a lot of people".

> they certainly can understand natural language sequences that are not present in their training data

Keeping the trained model as LLM in mind, I think learning a language includes generalization and is typically achieved by a human, so I'll try to formulate:

Can a trained LLM model learn languages that hasn't been in its training set just by chatting/prompting? Given that any Korean texts were excluded from the training set, could Korean be learned? Does that even work with languages descending from the same language family (Spanish in the training set but Italian should be learned)?