Is it possible to trigger an email to a customer after their review is posted and/or approved?

No, unfortunately that's not possible right now.  One of the limitations here is that for many Magento installations the customer is not even required to login in order to post a review, and so the review isn't actually linked to the customer account.  So there isn't any way of actually associating a posted review to a given customer.

Note: This may be something we add support for in the future.