Hi Sarah. Thanks for your question.
The Events Calendar plugin doesn’t collect any user information or affect WordPress’ user registration system.
The only way email addresses would be gathered is if you have our Community Events add-on (site visitors can add their own events to the site-wide calendar) or use our Event Tickets plugin for RSVP functionality. If you use our Event Tickets Plus add-on, you’ll need an e-commerce plugin (e.g. WooCommerce) to complete orders/purchases and they’d submit an email address to WooCommerce’s system.
However you determine to best use our free or paid plugins, please know that any email address that gets collected by WordPress user registration, our plugins, or an e-commerce plugin would be stored in the WordPress database and would therefore be available one way or another.
Last but not least, we have a pretty great Refund Policy so you can buy one or many of our add-ons and thoroughly test them.
I hope this information helped. Please let me know if you have any follow-up questions.