No, by default, the key contacts do not have access to the App.
An access can be set up by creating a specific role (e.g. "Task assignee") and assigning this role to key contacts.. The key contacts would then only see their tasks on the App.
You can find more details on how to create Key Contacts roles and assign them here.
If you still have questions about this topic or need help to set this up, don't hesitate to contact us by submitting a ticket.