LLMs in their current incarnation will not, but there's nothing inherently preventing them from learning. Contexts are getting large enough that having a sidecar database living with each project or individual as a sort of corpus of "shit I learned pairing with Justin" is already completely achievable, if only a product company wanted to do that.
Claude Plays Pokemon is kind of an interesting case study for this. This sort of knowledgebase is implemented, but even state of the art models struggle to use it effectively. They seem to fixate on small snippets from the knowledge base without any ability to consider greater context.