You can try calling this script everytime a new product is added, although then you wouldn't really do it in the "background"...
For more information, please note the question "How can I run a PHP script in the background after a form is submitted?"
EDIT:
If you wish to save the file on the server instead of outputting it to the browser, you can use different parameters. See also the html2pdf-wiki. Be aware that you cannot save the file on the user's computer unnoticed!
$html2pdf->Output('directory/file_xxxx.pdf', 'F');