Do we have to run Payment for all 0 amount invoices in 11i before the R12 upgrade?

We are doing some clean up for the Invoices preparing for R12.1.3 upgrade.  Some team member thinks that we should run 0 Payment for all  unpaid 0 amount Invoices.  I think that it is unnecessary because those invoices are 0 amount and they can be purged soon or later.   If we run the payment for those 0 amount invoices, the system would have many extract payment records. And the last_update_date for all those invoice would be the current date so we can not purged them for another 7 years.  That's why I think that we should not run 0 Payment for those 0 amount invoices.