Yes, Recurring Orders is fully compatible with MailChimp.
MailChimp is an email marketing service, sending over 10 billion marketing emails per month on behalf of its users. MailChimp integrates with all the major e-commerce providers so you can use your purchase data to send personalized campaigns and better understand how your marketing affects your bottom line.
When you Connect Your Shopify Store to MailChimp, all of the data will flow directly into your MailChimp list.
If a subscriber agrees to accept marketing during their checkout, they will be added to Shopify’s "Accepts Marketing" list. You can then export this list and import it into MailChimp. Alternatively, you can get the MailChimp for Shopify App which will automate this for you.
Just ensure you enable the Recurring Orders feature to Collect Email Addresses with Recurring Orders. Configure this setting to "Customer agrees to receive promotional emails by default" for optimal usage.
If you have any further questions on setting up MailChimp, Email their Support team.
Visit View and Export a List of Customers Who Accept Marketing for detailed instructions.