I want to be able to approve staff timesheets from smartphone allowing payroll officer to then process pay runs. is this possible?

Good day graysgrousegarde,
 

The mobile version has some limitations on the process that you can do.
 

 You can log in through a Web browser, so any action that you can take on a personal computer can be done on Mobile devices.

This ensures that information is properly recorded. Also, here's an article you can read to learn more about Timesheet setup: QuickBooks Online and TSheets.

Keep me posted if you need anything else. I'd be glad to help.