If I purchase one of the packages, can anyone who uses a link to my website generate PDFs without a banner?

Yes, after logging in to your Control Panel, you have the option of activating different hosts (example: www.meinserver.de).
For these hosts the Banner Add will not be shown in the PDF.

In order to determine the validation requests and decide whether they should be accepted or not, you have the option of checking and defining the URL to be rendered, the IP address or a special parameter.