We are considering having each branch/location release and print their own sales orders/invoices.  Our question is if branches are releasing invoices at the same time and branch A prints invoices will it pull/print all invoices  that have been released or only those from branch A.  We don't want branch A printing branch B's released sales orders.

Of course, Lorne is right.
 
However, if you have the ability to use Customer Class to define the branch, you can print Invoices by that criteria (assuming you are using a recent ISTS enhancement).