You’re close but not quite.
do_shortcode expects a string so give it one!
If function() returns a string you can
echo do_shortcode( '[shortcode]' . function() . '[/shortcode]' );
If function() directly outputs, you can capture its output using output buffering
//start the buffer
ob_start();
function(); //i.e pdf_print_popup();
//store out output buffer
$string = ob_get_contents();
//clear the buffer and close it
ob_end_clean();
and then use the string we stored
echo do_shortcode( '[shortcode]' . $string . '[/shortcode]' );