Neither integration is required to send emails from inside the CRM. The Transactional email add-on is used to send emails that would be triggered or generated from some other system, but send the emails through HubSpot’s email platform. The Gmail integration makes it easier to track and log emails in HubSpot when you’re sending emails using Gmail. Neither is a requirement for sending emails from inside the CRM app in HubSpot.
The Email and Sales dashboards are going to be the best way to see the overview of how well your emails are doing, including the number of emails being sent, and how many of those emails are being delivered, opened, or unsubscribed from.
There would not be a way to create and trigger an email from inside HubSpot, but have it sent through Mandrill, as we don’t have a way to get the contents of the email through the API.