No. Time tracking on tasks is not required. Time can be added at the project level. When starting a general timer the time will be applied at the project level by default, but it can be saved to a task as well.
Note: The only difference between tracking time on tasks vs projects is that tracking on tasks will give you more granular reporting. Track time on tasks if you require this level of detail.
Below is an example for adding general time:
And here is an example for adding task time: