A PDF will be saved with mime-type of application/pdf, so if your theme has an application.php or pdf.php template file that forces download (or if you check for mime-type in your attachment.php template), you can force a download.
A pdf.php file built like this in your theme should do the trick:
<?php if (have_posts()) : while (have_posts()) : the_post();
$pdf_title = $post->post_title;
$uploads_dir = wp_upload_dir();
$attachment_src = get_post_meta( $post->ID, '_wp_attached_file', true );
$pdf_src = path_join( $uploads_dir['path'], $attachment_src );
header("Pragma: public"); // required
header("Expires: 0");
header("Cache-Control: must-revalidate, post-check=0, pre-check=0");
header("Cache-Control: private",false); // required for certain browsers
header("Content-Type: application/pdf");
header("Content-Disposition: attachment; filename=\"".$pdf_title."\";" );
header("Content-Transfer-Encoding: binary");
header("Content-Length: ".filesize($pdf_src));
ob_clean();
flush();
readfile("$pdf_src");
endwhile; endif;
?>
(Edit: I should note that in order for this to work, when you insert the file into your post through the media uploader, you have to select Post URL rather than File URL in the Link URL field before inserting into your post. A link to a filename will follow the browser's preferences, but by linking to the WP post link, you can control its behaviour.)