Is there a fully functioning payroll system on the free download of Manager?
No, it is an accounting package with some payroll features such as manually entering payslip data and recording the payments to employees but it has no payroll calculation feature - see the guide Set up payslip items | Manager
Issue payslips | Manager
Set up and manage recurring payslips | Manager
and
Enter employees | Manager
Pay employees | Manager
The same features are available on the desktop, server, and cloud editions. Purchasing one of the paid versions gets you no additional capability beyond multiple users and remote access.
Thank you