Only if you pay for the priority service.  Postage Paid Australia stamps are only for account customers, they are just for convenience, you stamp the envelopes with the stamp, then hand them over the counter with your bulk postage form and the postage is charged to yor Auspost account at whatever rate applies to the service you request.  Priority service would only apply if you pay for priority so you would only use that stamp on those items you want sent at the priority rate.