The Batch Invoice concept and operation allows you to (and limits you to) post an identical list of charges to multiple customers without entering each invoice and then making copies. This precludes the ability to enter unique invoice information that is not pre-populated by QuickBooks. PO is not a calculated field but is merely a memo field and thus cannot be populated at all, even with same PO number for all customers in the batch.
The solution is to use the batch procedure to create all the invoices, and then open each one to add the PO