Summary:
The time can be transferred from Web TimeSheet to MS Project.
While transferring time from Web TimeSheet to MS Project using MSPI, 'Select Data to Update' tab plays a key role on how the data is updated/transferred to MS Project.
If the option 'Update Project Team', 'Resources and assignments' is checked, the user will be added to MS Project and subsequent time entries will be transferred from Web TimeSheet to MS Project.

(If the option 'Update Project Team', 'Resources and assignments' is not checked, then the transfer of the time will not occur from Web TimeSheet to MSP)

Note:
Other criterion also play an important role such as, selection of timesheet periods, approval status etc. The user's time will only be transferred if the user's direct assignment exists in the allowed list of Task Assignment in Web TimeSheet Project. Time entries coming through other assignments such as <All> or <Department> will not be transferred during time transfer from Web TimeSheet to MSP using MSPI.