Yes, when you navigate to the Contacts tab in Marketing Automation you can see a full list of customers who are currently being maintained in your account.
Clicking on an individual customer will take you to their Timeline which will show a detailed history of actions that were taken both within your booking platform as well as within Marketing Automation.
Examples of actions listed here would be:
Class reservations (either checked-in or no-showed)
Purchases made
Auto-Campaign Enrollments
You can also use the buttons located in the top right-hand side of this page to Email the customer directly, create an internal Note on their account, create a Task that's directly related to them, or create a Call Reminder for them.
Lastly, you can add a Marketing Automation tag on this customer's account by using the Tags drop-down in the bottom left-hand side of this page as well.
For more information on Tags, refer to the article here.