The Administrator role has the permission to Pay unapproved bills and therefore can schedule payments for a bill in any approval status. Even if a bill hasn't been approved yet, an Administrator can schedule a payment for that bill.
We present a notification when a user with Pay unapproved bills permissions starts to schedule a payment on a bill that hasn't been fully approved:
Single Bill Pay
Approval Status on a Paid Bill
A Paid bill will continue to reflect the approval status at the time of payment after the payment has been made. However, when viewing bills to approve we'll show payment status if a payment has been initiated:
Bulk Bill Approval
Single Bill Approval