Yes, the Auto Tracker feature seamlessly continues to track time even when navigating to various related tabs.
As an example if you have added the Auto Tracker component to the Cases object. The time tracking persists when accessing related tabs like TT details, Activities, Comments, Case history, etc., Even when interacting with these tabs—such as adding or viewing new TT details, activities, or comments the time continues to track.
Note: The timer stops tracking if you go to the list view, of an object from the Related tab by clicking View All string.