If your PDF is stored in a container, then you can script "Export Field Contents" to perform this action, and check the "automatically open file" checkbox to open the file.
If you are generating your PDF from a FileMaker layout (IE report), the same "automatically open file" checkbox is available.
Lastly, if you have a button, you can hardcode it with "Open URL" to launch a PDF file stored in a location accessible from the current user's computer (local drive, or shared drive).
So yes, on all accounts you can. This of course is assuming that adobe reader is set as the system default for opening PDFs.
If you have the container set to be interactive, then the FM-native option to export the field contents doesn't come up automatically, but Mike has given several workable options you can script. Just don't turn the entire field into the button to run the scripted process or you will lose the field's interactive properties.
If you have the field set for images rather than PDF interactivity, the PDF's first page will appear, and you can Control-click in the field to Export Field contents, which gives you an option in the dialog to automatically open the file when it exports.