Absence Management processing - general question

We have recently started using Absence Management with Time and Labor for a test group of 25 employees.  Eventually we would like to have all of our employees (~1500) on AM.  We were using the request leave through Time and Labor before this.    We have hourly and salaried employees.  Our pay period ends on a Friday.  Our payroll is processed on Tuesday and the departments have until 10:00 AM on Tuesday to finish their payroll.  Here is where my issue occurs:  if we have an hourly employee who is out Sick the Friday of the pay period end date and