That can be a bit difficult to track. How are you printing invoices? How do you track whether your customer print an invoice you send attached in an email?
Let say you have a way to track this, I would create a custom order attribute to flag orders and show it in a custom column in grid, look at this for example:
Mage_Sales_Controller_Abstract::printAction() to a place where set the attribute to true.
You can have your custom controller to handle your attribute flag and then redirect to
For more examples on printActions look in admin controllers at:
If you are using print functionality from backend then you can add the flag attribute and set the attribute by listening one of the events controller post/pre dispatch. Then show attribute in grid.
This is a good resource on how to add custom attributes to orders