Integrating Mandrill API for transaction emails

[Richard Holy]

Hello,

we have a Prestashop instance on a2hosting shared webhosting. The provider does not allow sending out emails via external SMTP servers. We would like to send Prestashop emails via Mandrill REST API (transactions, registrations...).
 

I have found this module: https://addons.prestashop.com/en/newsletter-sms/26887-mandrill-connector-transactional-email-from-mailchimp.html
The developer has not replied that but from the screenshots it looks that instead of using REST API, it uses the SMTP to send emails.

Has anyone tried to achieve the same? To send all the email via mandrill rest API? 
Would this be doable by creating a module or rewriting the core Mail::send() method?
Any suggestions?

Thank you,

Richard