Is it possible to configure Tiger, so that a user can download selected PDFs, but not images?

There's no built-in option that will do that.

You could embed a download link into the caption. Let's say your PDF is called mydog.pdf. In the comment, add something like:

Here's a <a href=“mydog.pdf” download>download link</a> for this PDF

Chrome automatically downloads the PDF - Firefox prompts the user to choose between saving and displaying it.