Can a Pending Approval Bill be posted even if it is not yet approved?

No, if that pending approval status is based on the standard Approval Status field

Like Luis said you could create a custom approval status field and then use the native status in another fashion

Note posting to GL only occurs when the transaction has been approved - native status (Bill, JE, Invoice)

Accounting managers nightmare… Check the impacting accounts(expense GL in P&L, per say) for that period. If the entry shows up it then you know the NS standard approval status are overridden with custom status.