Hey Will,
Thanks for reaching out. This is an interesting idea and it should be fairly simple to query for events of a certain tag, then include those in an email. (Check out this Knowledgebase guide for querying for events, for example → https://theeventscalendar.com/knowledgebase/using-tribe_get_events/)
You would have to use custom coding, of course, which is outside the scope of support even for folks with a premium license (https://theeventscalendar.com/knowledgebase/what-support-is-provided-for-license-holders/). But it is possible.
When it comes to specific plugins or apps to enable this, there are many options and none that we specifically recommend or discourage. MailPoet is a popular WordPress-powered email app, but there are also great WordPress integrations available via MailChimp/Mandrill, Campaign Monitor, SendGrid, and more.
I hope this information helps you move forward with your project!
— George