Yes you can, working on the same solution at the moment.
I would advice you to use fpdf. In the functions.php you create a new hook like this:
add_action( 'wpcf7_before_send_mail', 'save_application_form');
function save_application_form($cf7) {
/* GET EXTERNAL CLASSES */
require(TEMPLATEPATH.'/includes/fpdf.php');
/* example code to generate the pdf
$pdf = new FPDF();
$pdf->AddPage();
$pdf->SetFont('Arial','B',16);
$pdf->Write(5,"Hello, World!\n\n\n");
$pdf->Output(TEMPLATEPATH.'/file/pdf.pdf', 'F');
/* add the pdf as attach to the email
$cf7->uploaded_files = array ( 'attachedfile' => TEMPLATEPATH.'/file/pdf.pdf' );
}
Attention points: don’t forget to add [attachedfile] as parameter in the attachment field of your contact form
I have been searching for a long time scraping pieces of information together to solve this for myself.
Hope I can help you with this.
Eric