Hi Steve,
Some facilities including export to Google Calendar and subscription via iCal feeds are included – but what you’re describing, an email based system integrating a third party service like Mailchimp, isn’t covered by default.
It would certainly be possible to build a customization to facilitate this – and indeed The Events Calendar and its related plugins like Events Calendar PRO have been built with customization in mind, so they’re a great platform for this sort of thing.
Does that answer your questions?