Within AP * Configuration * Business Rules - currently "Require invoice approval before payment or posting" is all in one.
Suggestion - make approval and payment two separate approval items
This would make it possible to post AP invoices separate from the approval for payment
I think most organizations pay all invoices that have been approved. They may control which ones to pay by using the invoice due date during the payment process.
There already is a way to post an approved invoice but still not allow it to be paid. When approving invoices you can mark the Hold payment box.