John,
The URL would not be different. Because the document is stored in ArcGIS Online, the same sharing rules apply. If you share the document with the organization, then only members of the organization will be able to view it. If they are viewing from the ArcGIS.com website, they can go to the item, click the Open button to download a copy of the PDF.
If you are writing your own application to access the PDF, then your app will have to authenticate the user, then use a token to access the PDF item.
hope this helps,
Mike