Yes, you can track time for other TimeTracker users in your org. 

e.g: you can track time for your Manager, that does not have time to enter time manually.

Make sure that the TT user is created for the Manager also. Only then you will see their name in the Multiline Time Entry for adding their time details.

Create TT User by following the instructions here if the user is not created earlier.

To enter time for others

  • From the Multiline Time Entry tab, click the show list "Select TT User to create Timesheet Entry", and you see the list of TimeTracker users in your org. Select the user for whom you want to make the time entries. Enter the time details in the Multiline Time Entry screen and submit them.

You can enter up to 10 timesheet details at a time using the Multiline Time Entry screen. If there are more than 10 records, click the "Add 10 more Entries" string and click the Submit button.