Does the Task List disappear after all the tasks are completed?

Yes, the Task List disappears after the user completes all the tasks. To keep the Task List visible at all times, uncheck Task Progress under the Style section. This stops the progress bar from showing, but retains the Task List. For more information, see Configure a Task List.

Note:

If you don't select the Task Progress, the user will keep seeing the Task List, even after task completion.