The gallery only supports displaying Web maps and web mapping applications.
If your PDF is available on the web via a URL, as a hack, you could add it as a web mapping application. Then share the item to a group and ALSO make share the PDF publicly. Then from the group, you can click the Share button and create a gallery app. The PDF only downloads for me. I've not been able to get it to display in the browser window. There is a browser setting as part of a plug in or add in for handling PDFs, but it didn't work for me.
THanks,
Mike