Unless your SME is building new content to feed the LLM, LLMs won't be able to produce anything specific to your organization. All they can do is write up common knowledge. Which is not any more helpful in transferring institutional knowledge than a search engine.
The only way for constant knowledge transfer to exist is to have documentation and collaboration be a core tenet of your organizational culture. It is a social problem, not a tech problem.
Employees are not motivated to do knowledge transfer. It goes directly against their job security. You need to motivate them somehow, and I’m not sure how you would achieve that.