Could it be possible to train LLM only through the chat messages without any other data or input?

If Guppy doesn't know regular expressions yet, could I teach it to it just by conversation? It's a fish so it wouldn't probably understand much about my blabbing, but would be interesting to give it a try.

Or is there some hard architectural limit in the current LLM's, that the training needs to be done offline and with fairly large training set.