Yes, you can make sure that the app is automatically pinned in the employee's Teams client.
Previously it has been possible to pin the Myfone Teams app on behalf of the employees as a part of setting up Teams call functionality from Flexfone. It is no longer possible to pin the app as a part of setting up the Teams call functionality, but you can still do it manually from the Teams admin center.
You find a guide from Microsoft here.
Use the app without call functionality
Although you don't have Teams call functionality, you can benefit from the Myfone Teams app. Through the app you have a great overview of the different phone queues and colleagues, and the app allows you to acces all the company's contacts, information about colleagues and their calendars among other things.