- You have many patron accounts loaded without an IllId associated with them and you need to find a way to get them added
No, provision-on-demand only creates patron accounts which contain the name, email address and NameID from your Identity Provider. The NameID from their IdP corresponds with the User ID at Source.
Instead, you'll need to update them using a patron load. As long as the patron load contains the correct sourceSystem and idAtSource to match on, you can add the ILL ID field to those files using a patron load. The matching rules will look for these two fields first.
Patron load matching rules exist.